Fixpoint subseq {A} (xs ys : list A) : Prop :=
  match xs, ys with
    | [], _ => True
    | x :: xs', y :: ys' => (x = y /\ subseq xs' ys') \/ subseq xs ys'
    | _, _ => False
  end.

Lemma subseq_app_tail : forall ys xs zs, subseq (A:=A) xs ys -> subseq (xs ++ zs) (ys ++ zs).