induction i using natBelow_rect in v |- *.
simpl.
intros.
rewrite (eq_cons v).
simpl head.
left...
intros.
rewrite (eq_cons v).
right.
simpl plus.
fold (Snb (mkNatBelow v0 p)).
rewrite nth_S...
Qed.

(* Specifications: *)
Lemma to_list_app A n (v: Vector.t A n) m (w: Vector.t A m):
to_list (app v w) = List.app (to_list v) (to_list w).