proposition: Lemma app_nth1 : forall l l' d n, n < length l -> nth n (l++l') d = nth n l d.
proof: Proof. intro l; induction l as [|? ? IHl]. - inversion 1. - intros l' d [|n]; simpl; [intros; reflexivity|]. intros H. apply IHl. now apply Nat.succ_lt_mono. Qed.
imports: PeanoNat