%
\begin{isabellebody}%
\setisabellecontext{FC{\isadigit{6}}{\isacharunderscore}Status}%
%
\isamarkupsection{FC status proofs%
}
\isamarkuptrue%
%
\isadelimtheory
%
\endisadelimtheory
%
\isatagtheory
\isacommand{theory}\isamarkupfalse%
\ FC{\isadigit{6}}{\isacharunderscore}Status\isanewline
\isakeyword{imports}\ FC{\isadigit{6}}{\isacharunderscore}Data\ SomeShareNegativeImpl\ WeightsShares{\isacharunderscore}NotFCFamily\ FCTactics\isanewline
\isakeyword{begin}%
\endisatagtheory
{\isafoldtheory}%
%
\isadelimtheory
%
\endisadelimtheory
\isanewline
\isanewline
\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ \ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{8}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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t}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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t}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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t}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{7}}{\isadigit{0}}{\isadigit{4}}{\isadigit{1}}{\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isadigit{8}}{\isadigit{5}}{\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isadigit{8}}{\isadigit{5}}{\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isadigit{8}}{\isadigit{3}}{\isadigit{7}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isadigit{7}}{\isadigit{0}}{\isadigit{9}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isadigit{7}}{\isadigit{0}}{\isadigit{9}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{4}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{8}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{8}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{6}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{8}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{7}}{\isadigit{9}}{\isadigit{6}}{\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{7}}{\isadigit{8}}{\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isadigit{8}}{\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{4}}{\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{4}}{\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isadigit{5}}{\isadigit{3}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{0}}{\isadigit{2}}{\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{4}}{\isadigit{7}}{\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{4}}{\isadigit{7}}{\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{1}}{\isadigit{3}}{\isadigit{9}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isadigit{2}}{\isadigit{6}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{1}}{\isadigit{6}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{9}}{\isadigit{2}}{\isadigit{4}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{0}}{\isadigit{7}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{0}}{\isadigit{7}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isadigit{7}}{\isadigit{9}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{2}}{\isadigit{4}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{1}}{\isadigit{7}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{2}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{0}}{\isadigit{3}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{8}}{\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{8}}{\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{8}}{\isadigit{3}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{9}}{\isadigit{3}}{\isadigit{2}}{\isadigit{5}}{\isadigit{9}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{9}}{\isadigit{3}}{\isadigit{1}}{\isadigit{8}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isadigit{7}}{\isadigit{1}}{\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isadigit{6}}{\isadigit{2}}{\isadigit{7}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isadigit{9}}{\isadigit{2}}{\isadigit{4}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isadigit{1}}{\isadigit{2}}{\isadigit{6}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{7}}{\isadigit{9}}{\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isadigit{5}}{\isadigit{0}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isadigit{5}}{\isadigit{8}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isadigit{4}}{\isadigit{3}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{4}}{\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{0}}{\isadigit{1}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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t}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{7}}{\isadigit{8}}{\isadigit{3}}{\isadigit{5}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isadigit{5}}{\isadigit{2}}{\isadigit{0}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{6}}{\isadigit{4}}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{7}}{\isadigit{2}}{\isadigit{9}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isadigit{6}}{\isadigit{1}}{\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{8}}{\isadigit{9}}{\isadigit{0}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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t}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{8}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{8}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{8}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{6}}{\isadigit{5}}{\isadigit{4}}{\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{2}}{\isadigit{5}}{\isadigit{9}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{7}}{\isadigit{2}}{\isadigit{6}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{1}}{\isadigit{6}}{\isadigit{8}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{5}}{\isadigit{3}}{\isadigit{0}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{1}}{\isadigit{3}}{\isadigit{3}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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sacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{9}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{9}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{7}}{\isadigit{3}}{\isadigit{7}}{\isadigit{6}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{3}}{\isadigit{7}}{\isadigit{6}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isadigit{8}}{\isadigit{8}}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isadigit{3}}{\isadigit{8}}{\isadigit{6}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{4}}{\isadigit{2}}{\isadigit{2}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isadigit{9}}{\isadigit{8}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{1}}{\isadigit{4}}{\isadigit{7}}{\isadigit{6}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{3}}{\isadigit{3}}{\isadigit{4}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{4}}{\isadigit{7}}{\isadigit{2}}{\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{9}}{\isadigit{5}}{\isadigit{4}}{\isadigit{7}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{1}}{\isadigit{9}}{\isadigit{0}}{\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isadigit{3}}{\isadigit{6}}{\isadigit{7}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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on}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{0}}{\isadigit{4}}{\isadigit{4}}{\isadigit{0}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isadigit{8}}{\isadigit{7}}{\isadigit{4}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{6}}{\isadigit{5}}{\isadigit{9}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{2}}{\isadigit{1}}{\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isadigit{5}}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isadigit{4}}{\isadigit{7}}{\isadigit{9}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{5}}{\isadigit{6}}{\isadigit{6}}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{6}}{\isadigit{9}}{\isadigit{9}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isadigit{9}}{\isadigit{3}}{\isadigit{2}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{5}}{\isadigit{6}}{\isadigit{0}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{1}}{\isadigit{6}}{\isadigit{8}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isadigit{3}}{\isadigit{6}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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on}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{5}}{\isadigit{9}}{\isadigit{4}}{\isadigit{0}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{5}}{\isadigit{2}}{\isadigit{2}}{\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isadigit{0}}{\isadigit{4}}{\isadigit{6}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isadigit{8}}{\isadigit{0}}{\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{1}}{\isadigit{0}}{\isadigit{8}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{8}}{\isadigit{8}}{\isadigit{6}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{6}}{\isacharcomma}\ {\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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it{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{6}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{9}}{\isadigit{7}}{\isadigit{7}}{\isadigit{5}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{6}}{\isadigit{6}}{\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{4}}{\isadigit{7}}{\isadigit{6}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{0}}{\isadigit{7}}{\isadigit{6}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{6}}{\isadigit{0}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isadigit{4}}{\isadigit{4}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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eright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{9}}{\isadigit{9}}{\isadigit{6}}{\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{7}}{\isadigit{9}}{\isadigit{9}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isadigit{1}}{\isadigit{4}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{5}}{\isadigit{8}}{\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{0}}{\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isadigit{1}}{\isadigit{6}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{9}}{\isadigit{7}}{\isadigit{0}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{5}}{\isadigit{2}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{8}}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{5}}{\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isadigit{1}}{\isadigit{6}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isadigit{1}}{\isadigit{6}}{\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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on}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{6}}{\isadigit{9}}{\isadigit{3}}{\isadigit{6}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isadigit{4}}{\isadigit{3}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isadigit{3}}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{5}}{\isadigit{3}}{\isadigit{3}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{4}}{\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{0}}{\isadigit{2}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{9}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{7}}{\isadigit{3}}{\isadigit{6}}{\isadigit{6}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{7}}{\isadigit{7}}{\isadigit{7}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{5}}{\isadigit{1}}{\isadigit{9}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{7}}{\isadigit{9}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{3}}{\isadigit{0}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{4}}{\isadigit{2}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{9}}{\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isadigit{3}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{8}}{\isadigit{0}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{5}}{\isadigit{1}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{8}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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eright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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it{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{7}}{\isadigit{8}}{\isadigit{2}}{\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{1}}{\isadigit{1}}{\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{0}}{\isadigit{6}}{\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{6}}{\isadigit{5}}{\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{8}}{\isadigit{6}}{\isadigit{3}}{\isadigit{9}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{7}}{\isadigit{9}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{6}}{\isadigit{0}}{\isadigit{8}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isadigit{8}}{\isadigit{6}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isadigit{8}}{\isadigit{6}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isadigit{1}}{\isadigit{6}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{9}}{\isadigit{0}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isadigit{1}}{\isadigit{6}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{6}}{\isadigit{2}}{\isadigit{6}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isadigit{2}}{\isadigit{6}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isadigit{6}}{\isadigit{0}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isadigit{3}}{\isadigit{5}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{4}}{\isadigit{5}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{6}}{\isadigit{3}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{9}}{\isadigit{7}}{\isadigit{2}}{\isadigit{3}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isadigit{4}}{\isadigit{1}}{\isadigit{2}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{5}}{\isadigit{6}}{\isadigit{1}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isadigit{2}}{\isadigit{5}}{\isadigit{7}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isadigit{2}}{\isadigit{0}}{\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isadigit{6}}{\isadigit{7}}{\isadigit{9}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{7}}{\isadigit{7}}{\isadigit{6}}{\isadigit{7}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{7}}{\isadigit{6}}{\isadigit{7}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{6}}{\isadigit{0}}{\isadigit{4}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{5}}{\isadigit{1}}{\isadigit{5}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{5}}{\isadigit{1}}{\isadigit{5}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{6}}{\isadigit{0}}{\isadigit{4}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{1}}{\isadigit{9}}{\isadigit{9}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{9}}{\isadigit{6}}{\isadigit{6}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isadigit{3}}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isadigit{2}}{\isadigit{7}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isadigit{9}}{\isadigit{6}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{3}}{\isadigit{7}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ 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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{0}}{\isadigit{8}}{\isadigit{5}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{3}}{\isadigit{0}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{9}}{\isadigit{3}}{\isadigit{0}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{2}}{\isadigit{5}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{8}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{0}}{\isadigit{2}}{\isadigit{5}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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on}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{2}}{\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{6}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{3}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{0}}{\isadigit{5}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ 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a}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{8}}{\isadigit{4}}{\isadigit{2}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{3}}{\isadigit{8}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isadigit{4}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isadigit{4}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{6}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{6}}{\isadigit{6}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{4}}{\isacharcomma}\ {\isadigit{3}}{\isacharcomma}\ {\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{4}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{4}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{5}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{1}}{\isadigit{8}}{\isacharcomma}\ {\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{6}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{0}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{8}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{2}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbrac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set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ 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a}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ 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a}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{7}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{8}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{7}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{8}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{7}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{3}}{\isacharcomma}\ {\isadigit{8}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{7}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{7}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{8}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{6}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{6}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{5}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{5}}{\isadigit{1}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{5}}{\isacharcomma}\ {\isadigit{1}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{9}}{\isacharcomma}\ {\isadigit{4}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{6}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{3}}{\isadigit{7}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{1}}{\isadigit{0}}{\isacharcomma}\ {\isadigit{1}}{\isadigit{4}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{1}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ {\isacharbrackleft}simp{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isacharparenright}{\isachardoublequoteclose}\ {\isacharparenleft}\isakeyword{is}\ {\isachardoublequoteopen}{\isasymnot}\ FC{\isacharunderscore}family\ {\isacharquery}Fc{\isachardoublequoteclose}{\isacharparenright}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{1}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{2}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{3}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{4}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs{\isadigit{5}}\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbraceleft}{\isacharbraceleft}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharcomma}{\isacharbraceleft}{\isadigit{0}}{\isacharcomma}{\isadigit{1}}{\isacharcomma}{\isadigit{2}}{\isacharcomma}{\isadigit{3}}{\isacharcomma}{\isadigit{4}}{\isacharcomma}{\isadigit{5}}{\isacharbraceright}{\isacharbraceright}{\isacharcolon}{\isacharcolon}nat\ set\ set{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}Fs\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isacharquery}Fs{\isadigit{1}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{2}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{3}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{4}}{\isacharcomma}\ {\isacharquery}Fs{\isadigit{5}}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{let}\isamarkupfalse%
\ {\isacharquery}c\ {\isacharequal}\ {\isachardoublequoteopen}{\isacharbrackleft}{\isadigit{1}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{7}}{\isacharcomma}\ {\isadigit{3}}{\isadigit{6}}{\isacharcomma}\ {\isadigit{2}}{\isacharcomma}\ {\isadigit{2}}{\isadigit{8}}{\isacharbrackright}\ {\isacharcolon}{\isacharcolon}\ nat\ list{\isachardoublequoteclose}\isanewline
\ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \isacommand{proof}\isamarkupfalse%
\ {\isacharparenleft}rule\ nonFC{\isacharbrackleft}\isakeyword{where}\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ \isakeyword{and}\ c\ {\isacharequal}\ {\isacharquery}c{\isacharbrackright}{\isacharparenright}\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ {\isacharquery}Fs{\isachardot}\ F\ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{proof}\isamarkupfalse%
{\isacharminus}\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{1}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{2}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{3}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{4}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{moreover}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{have}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isacharquery}Fs{\isadigit{5}}\ \ {\isasymin}\ {\isasymlbrace}{\isacharquery}Fc{\isasymrbrace}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}extension{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \ \ \ \ \isacommand{ultimately}\isamarkupfalse%
\isanewline
\ \ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isacharquery}thesis\isanewline
\ \ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ union{\isacharunderscore}closed{\isacharunderscore}extensions{\isacharunderscore}def{\isacharparenright}\isanewline
\ \ \ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}let\ Fs\ {\isacharequal}\ {\isacharquery}Fs\ in\ {\isasymforall}\ a\ {\isasymin}\ {\isasymUnion}\ {\isacharquery}Fc{\isachardot}\ sum{\isacharunderscore}list\ {\isacharparenleft}map\ {\isacharparenleft}{\isasymlambda}\ {\isacharparenleft}x{\isacharcomma}\ y{\isacharparenright}{\isachardot}\ int\ x\ {\isacharasterisk}\ y{\isacharparenright}\ {\isacharparenleft}zip\ {\isacharquery}c\ {\isacharparenleft}map\ {\isacharparenleft}frankl{\isacharunderscore}fun\ a{\isacharparenright}\ Fs{\isacharparenright}{\isacharparenright}{\isacharparenright}\ {\isacharless}\ {\isadigit{0}}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ nonFC{\isacharunderscore}is{\isacharunderscore}system{\isacharunderscore}solution{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ %
\isaantiq
term\ {\isachardoublequote}{\isacharbrackleft}{\isadigit{0}}{\isachardot}{\isachardot}{\isacharless}{\isadigit{6}}{\isacharbrackright}{\isacharcolon}{\isacharcolon}nat\ list{\isachardoublequote}{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\ \isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymexists}wj{\isasymin}List{\isachardot}set\ {\isacharquery}c{\isachardot}\ {\isadigit{0}}\ {\isacharless}\ wj{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}length\ {\isacharquery}c\ {\isacharequal}\ length\ {\isacharquery}Fs{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}finite\ {\isacharparenleft}{\isasymUnion}\ {\isacharquery}Fc{\isacharparenright}{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ auto\isanewline
\ \ \isacommand{next}\isamarkupfalse%
\isanewline
\ \ \ \ \ \isacommand{show}\isamarkupfalse%
\ {\isachardoublequoteopen}union{\isacharunderscore}closed\ {\isacharquery}Fc{\isachardoublequoteclose}\isanewline
\ \ \ \ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}tactic\ {\isacharverbatimopen}\ union{\isacharunderscore}closed{\isacharunderscore}tac\ %
\isaantiq
context{}%
\endisaantiq
\ {\isadigit{1}}\ {\isacharverbatimclose}{\isacharparenright}\isanewline
\ \ \isacommand{qed}\isamarkupfalse%
\isanewline
\isacommand{qed}\isamarkupfalse%
%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
\isanewline
\isanewline
\isanewline
\isanewline
\isanewline
\isanewline
\isanewline
\isanewline
\isacommand{theorem}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymforall}\ F\ {\isasymin}\ set\ nonFC{\isadigit{6}}{\isachardot}\ {\isasymnot}\ FC{\isacharunderscore}family\ {\isacharparenleft}f{\isacharunderscore}to{\isacharunderscore}set{\isacharunderscore}l\ F{\isacharparenright}{\isachardoublequoteclose}\isanewline
%
\isadelimproof
%
\endisadelimproof
%
\isatagproof
\isacommand{unfolding}\isamarkupfalse%
\ nonFC{\isadigit{6}}{\isacharunderscore}def\isanewline
\isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}simp\ del{\isacharcolon}\ One{\isacharunderscore}nat{\isacharunderscore}def{\isacharparenright}%
\endisatagproof
{\isafoldproof}%
%
\isadelimproof
\isanewline
%
\endisadelimproof
%
\isadelimtheory
\isanewline
%
\endisadelimtheory
%
\isatagtheory
\isacommand{end}\isamarkupfalse%
%
\endisatagtheory
{\isafoldtheory}%
%
\isadelimtheory
%
\endisadelimtheory
%
\end{isabellebody}%
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