Theorem zltle ≪ | index | src | ≫

theorem zltle (a b: nat): $ a  a <=Z b $;

Step	Hyp	Ref	Expression
1		zltnle	a <Z b <-> ~b <=Z a
2		zleorle	b <=Z a \/ a <=Z b
3	2	conv or	~b <=Z a -> a <=Z b
4	1, 3	sylbi	a <Z b -> a <=Z 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)