Theorem zle02eq ≪ | index | src | ≫

theorem zle02eq (a: nat): $ 0 <=Z a <-> a = b0 (a // 2) $;

Step	Hyp	Ref	Expression
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	2	bitr*	(~odd a <-> a = b0 (a // 2)) -> (0 <=Z a <-> a = b0 (a // 2))
4		eqb0	~odd a <-> a = b0 (a // 2)
5	2, 4	bitr*	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)