Proof using.
induction xs; intros; destruct ys; simpl in *;
intuition eauto using f_equal2, subseq_cons_drop.
exfalso.
repeat find_apply_lem_hyp subseq_length.
simpl in *. omega.
Qed.

(* Specifications: *)
Lemma subseq_filter :
forall (f : A -> bool) xs,
subseq (filter f xs) xs.