
The complete proof:
The Isar proof is in: proofs/isar_proof12.thy
The proof in the natural language form is in: proofs/nl_proof12.tex
The number of steps: 2
The number of axioms used: 1
The list of used axioms:
ax_ncol_312 

The clean proof: 
The Isar proof is in: proofs/isar_proof_optimized12.thy
The proof in the natural language form is in: proofs/nl_proof_optimized12.tex
The number of steps: 2

The list of all axioms considered (given and derived) is in: all_axioms.txt.

Basic time: 0 seconds. 
Cleaning time: 0.01 seconds. 
Total time: 0.01 seconds. 

