
The complete proof:
The Isar proof is in: proofs/isar_proof6.thy
The proof in the natural language form is in: proofs/nl_proof6.tex
The number of steps: 30
The number of axioms used: 4
The list of used axioms:
ax_D3 ax_D8a ax_g5 ax_D7 

The clean proof: 
The Isar proof is in: proofs/isar_proof_optimized6.thy
The proof in the natural language form is in: proofs/nl_proof_optimized6.tex
The number of steps: 20

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

Basic time: 0.02 seconds. 
Cleaning time: 0.01 seconds. 
Total time: 0.03 seconds. 

