Theorem appendnth2 ≪ | index | src | ≫

theorem appendnth2 (i l1 l2: nat):
  $ len l1 <= i -> nth i (l1 ++ l2) = nth (i - len l1) l2 $;

Step	Hyp	Ref	Expression
1		appendnth2_	nth (len l1 + (i - len l1)) (l1 ++ l2) = nth (i - len l1) l2
2		pncan3	len l1 <= i -> len l1 + (i - len l1) = i
3	2	eqcomd	len l1 <= i -> i = len l1 + (i - len l1)
4	3	ntheq1d	len l1 <= i -> nth i (l1 ++ l2) = nth (len l1 + (i - len l1)) (l1 ++ l2)
5	1, 4	syl6eq	len l1 <= i -> nth i (l1 ++ l2) = nth (i - len l1) l2

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)