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

Lemma NoDup_incl_Permutation (A: Set) n (a b: Vector.t A n):
List.NoDup a -> List.incl a b -> Permutation a b.