Proof using.
induction xs; simpl; intros; destruct xs'.
- auto.
- subst. simpl in *. find_inversion.
invc H. exfalso. rewrite map_app in *. simpl in *.
repeat find_rewrite. intuition.
- subst. simpl in *. find_inversion.
invc H. exfalso. rewrite map_app in *. simpl in *.
repeat find_rewrite. intuition.
- subst. simpl in *. find_injection. intros. subst.
f_equal. eapply IHxs; eauto. solve_by_inversion.
Qed.

Lemma filter_NoDup :
forall p (l : list A),
NoDup l ->
NoDup (filter p l).