Theorem ltcons2 ≪ | index | src | ≫

theorem ltcons2 (a b c: nat): $ b < c <-> a : b < a : c $;

Step	Hyp	Ref	Expression
1		bitr	(b < c <-> a, b < a, c) -> (a, b < a, c <-> a : b < a : c) -> (b < c <-> a : b < a : c)
2		ltpr2	b < c <-> a, b < a, c
3	1, 2	ax_mp	(a, b < a, c <-> a : b < a : c) -> (b < c <-> a : b < a : c)
4		ltsuc	a, b < a, c <-> suc (a, b) < suc (a, c)
5	4	conv cons	a, b < a, c <-> a : b < a : c
6	3, 5	ax_mp	b < c <-> a : b < a : c

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)