
The complete proof:
The Isar proof is in: proofs/isar_proof4.thy
The proof in the natural language form is in: proofs/nl_proof4.tex
The number of steps: 43
The number of axioms used: 4
The list of used axioms:
ax_D1 ax_D6a ax_g1 ax_g4 

The clean proof: 
The Isar proof is in: proofs/isar_proof_optimized4.thy
The proof in the natural language form is in: proofs/nl_proof_optimized4.tex
The number of steps: 12

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

Basic time: 0.12 seconds. 
Cleaning time: 0.02 seconds. 
Total time: 0.14 seconds. 

