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_remove_all : forall (ds l l' : list A), subseq l l' -> subseq (remove_all A_eq_dec ds l) l'.