Proof using.
induction l; intros.
- auto.
- simpl. invc_NoDup. constructor.
+ intro. do_in_app. intuition eauto with *.
+ intuition eauto with *.
Qed.

Lemma NoDup_map_partition :
forall (f : A -> B) xs l y zs xs' y' zs',
NoDup (map f l) ->
l = xs ++ y :: zs ->
l = xs' ++ y' :: zs' ->
f y = f y' ->
xs = xs'.