Proof with auto.
unfold compose.
induction l...
intros.
simpl.
rewrite IHl.
destruct (p a); simpl...
Qed.

(* Specifications: *)
Lemma count_filtered X (p q: X -> bool):
(forall x, q x = true -> p x = false) ->
forall l, count p (filter q l) = 0.