Theorem ltconsid1 ≪ | index | src | ≫

theorem ltconsid1 (a b: nat): $ a < a : b $;

Step	Hyp	Ref	Expression
1		leltsuc	a <= a, b <-> a < suc (a, b)
2	1	conv cons	a <= a, b <-> a < a : b
3		leprid1	a <= a, b
4	2, 3	mpbi	a < 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)