Theorem sub1can ≪ | index | src | ≫

theorem sub1can (a: nat): $ a != 0 -> suc (a - 1) = a $;

Step	Hyp	Ref	Expression
1		le11	1 <= a <-> a != 0
2		add12	a - 1 + 1 = suc (a - 1)
3		npcan	1 <= a -> a - 1 + 1 = a
4	2, 3	syl5eqr	1 <= a -> suc (a - 1) = a
5	1, 4	sylbir	a != 0 -> suc (a - 1) = 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_set (elab, ax_8), axs_the (theid, the0), axs_peano (peano1, peano2, peano5, addeq, add0, addS)