Definition plusnb (y x: nat) (nb: natBelow x): natBelow (x + y) :=
  match nb in natBelow x' return natBelow (x' + y) with
  | mkNatBelow a b => eq_rec_r natBelow (mkNatBelow a (b + y)) (eq_S _ _ (plus_assoc_reverse a b y))
  end.

Lemma map_app (A B: Type) (f: A -> B) n (v: Vector.t A n) m (w: Vector.t A m): map f (app v w) = app (map f v) (map f w).