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

Lemma S_rect A n (P: Vector.t A (S n) -> Type):
(forall h t, P (Vector.cons h t)) -> forall v, P v.