Theorem ltnle ≪ | index | src | ≫

theorem ltnle (a b: nat): $ a < b <-> ~b <= a $;

Step	Hyp	Ref	Expression
1		ltlenle	a < b <-> a <= b /\ ~b <= a
2		anr	a <= b /\ ~b <= a -> ~b <= a
3	1, 2	sylbi	a < b -> ~b <= a
4		leorlt	b <= a \/ a < b
5	4	conv or	~b <= a -> a < b
6	3, 5	ibii	a < b <-> ~b <= a

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_peano (peano1, peano2, peano5, addeq, add0, addS)