intuition.
eapply H.
eapply vector_cons_eq.
eauto.
Qed.

Lemma map_NoDup : forall (A B : Set)(ls : list A)(f : A -> B),
NoDup ls ->
(forall a1 a2, a1 <> a2 -> (f a1) <> (f a2)) ->
NoDup ((map f) ls).