(* 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 listRepeat_length : forall n (A : Type) (a : A), length (listRepeat a n) = n.