Theorem zle02eq ≪ | index | src | ≫ 

theorem zle02eq (a: nat): $ 0 <=Z a <-> a = b0 (a // 2) $;
StepHypRefExpression
1 bitr 
(0 <=Z a <-> ~odd a) -> (~odd a <-> a = b0 (a // 2)) -> (0 <=Z a <-> a = b0 (a // 2))
2 zle02 
0 <=Z a <-> ~odd a
3 1, 2 ax_mp 
(~odd a <-> a = b0 (a // 2)) -> (0 <=Z a <-> a = b0 (a // 2))
4 eqb0 
~odd a <-> a = b0 (a // 2)
5 3, 4 ax_mp 
0 <=Z a <-> a = b0 (a // 2)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)