Proof using.
induction l; intros.
- auto.
- invc_NoDup. simpl. break_if; auto.
constructor; auto.
intro. apply filter_In in H. intuition.
Qed.

Lemma NoDup_map_filter :
forall (f : A -> B) g l,
NoDup (map f l) ->
NoDup (map f (filter g l)).