induction v.
intros.
inversion H.
intros.
inversion_clear H.
exists (nb0 n).
simpl...
destruct (IHv H0).
exists (Snb x).
rewrite nth_S...
Qed.

Lemma eq_app_inv A n m (a b: Vector.t A n) (c d: Vector.t A m): app a c = app b d -> a = b /\ c = d.
Proof with auto.