Ltac ifeq :=
    match goal with
      [ H : context [ eq_nat_dec ?x ?x ] |- _ ] => destruct (eq_nat_dec x x) as [_|]; [|congruence]
    | [ |- context [ eq_nat_dec ?x ?x ] ] => destruct (eq_nat_dec x x) as [_|]; [|congruence]
    | [ H : context [ eq_nat_dec ?x ?y ] |- _ ] => destruct (eq_nat_dec x y)
    | [ |- context [ eq_nat_dec ?x ?y ] ] => destruct (eq_nat_dec x y)
    end.

Lemma nth_snoc {A} i (l : list A) x : i <> List.length l -> nth (l ++ x :: nil) i = nth l i.