Theorem nthlfn ≪ | index | src | ≫

theorem nthlfn (F: set) (i n: nat): $ i < n -> nth i (lfn F n) = suc (F @ i) $;

Step	Hyp	Ref	Expression
1		suceq	F @ (0 + i) = F @ i -> suc (F @ (0 + i)) = suc (F @ i)
2		appeq2	0 + i = i -> F @ (0 + i) = F @ i
3		add01	0 + i = i
4	2, 3	ax_mp	F @ (0 + i) = F @ i
5	1, 4	ax_mp	suc (F @ (0 + i)) = suc (F @ i)
6		lfnauxnth	i < n -> nth i (lfnaux F 0 n) = suc (F @ (0 + i))
7	6	conv lfn	i < n -> nth i (lfn F n) = suc (F @ (0 + i))
8	5, 7	syl6eq	i < n -> nth i (lfn F n) = suc (F @ i)

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)