induction v; intros.
apply sorted_one.
apply sorted_more...
apply H. left...
Qed.

(* Specifications: *)
Lemma sorted_cons_inv x n (v: Vector.t X (S n)): sorted (Vector.cons x v) -> Xle x (head v).
Lemma sorted_app (v w: List.list X): sorted v -> sorted w ->
(forall x y, List.In x v -> List.In y w -> Xle x y) -> sorted (List.app v w).