(* 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_permutation : forall (A : Set)(P : A -> Prop)(ls1 ls2 : list A), Permutation ls1 ls2 -> forall c, pred_count P ls1 c -> pred_count P ls2 c.