Proof with auto.
intros.
rewrite <- List_map in H.
destruct (In_map_inv H). clear H.
destruct H0.
rewrite <- (natBelow_unique _ _ H)...
Qed.

(* Specifications: *)
Lemma In_nats_0 n x: List.In x (nats 0 n).
Lemma S_rect A n (P: Vector.t A (S n) -> Type):
(forall h t, P (Vector.cons h t)) -> forall v, P v.
Lemma NoDup_incl_Permutation (A: Set) n (a b: Vector.t A n):
List.NoDup a -> List.incl a b -> Permutation a b.