Theorem zleb0 ≪ | index | src | ≫

theorem zleb0 (a b: nat): $ b0 a <=Z b0 b <-> a <= b $;

Step	Hyp	Ref	Expression
1		bitr4	(b0 a <=Z b0 b <-> ~b < a) -> (a <= b <-> ~b < a) -> (b0 a <=Z b0 b <-> a <= b)
2		noteq	(b0 b <Z b0 a <-> b < a) -> (~b0 b <Z b0 a <-> ~b < a)
3	2	conv zle	(b0 b <Z b0 a <-> b < a) -> (b0 a <=Z b0 b <-> ~b < a)
4		zltb0	b0 b <Z b0 a <-> b < a
5	3, 4	ax_mp	b0 a <=Z b0 b <-> ~b < a
6	1, 5	ax_mp	(a <= b <-> ~b < a) -> (b0 a <=Z b0 b <-> a <= b)
7		lenlt	a <= b <-> ~b < a
8	6, 7	ax_mp	b0 a <=Z b0 b <-> a <= b

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)