Proof using.
induction ys; intros.
- destruct xs; simpl in *; intuition.
- simpl in *. invc_NoDup.
break_match.
+ constructor.
+ intuition.
subst. constructor; eauto using subseq_In.
Qed.

(* Specifications: *)
Lemma subseq_remove :
forall (x : A) xs,
subseq (remove A_eq_dec x xs) xs.