Proof with reflexivity.
induction n; intros.
rewrite (eq_nil v)...
rewrite (eq_cons v).
simpl.
rewrite IHn...
Qed.

(* Specifications: *)
Lemma app_eq A m (x x': Vector.t A m) n (y y': Vector.t A n): x = x' -> y = y' -> app x y = app x' y'.
Lemma nb_nats_plus x n y: nb_nats n (x + y) = app (nb_nats n x) (nb_nats (n + x) y).
Proof with auto.