(* listRepeat is used to show some interesting properties of rel_map and pred_count. *)
Fixpoint listRepeat(A : Type)(a : A) n :=
  match n with
    | 0 => nil
    | S n' => a :: (listRepeat a n')
  end.

Lemma pred_count_eq_none_inv : forall (A : Set)(P : A -> Prop)(ls : list A) c, pred_count P ls c -> (forall a, In a ls -> ~P a) -> c = O.