Theorem nthSlt ≪ | index | src | ≫

theorem nthSlt (a l n: nat): $ nth n l = suc a -> n < len l $;

Step	Hyp	Ref	Expression
1		nthne0	nth n l != 0 <-> n < len l
2		sucne0	nth n l = suc a -> nth n l != 0
3	1, 2	sylib	nth n l = suc a -> n < len l

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), axs_peano (peano1)