(*********)
Definition Rabs r : R :=
  match Rcase_abs r with
    | left _ => - r
    | right _ => r
  end.

(* Specifications: *)
Lemma Rabs_R0 : Rabs 0 = 0.
Lemma Rabs_R1 : Rabs 1 = 1.
Lemma Rabs_no_R0 : forall r, r <> 0 -> Rabs r <> 0.
Lemma Rabs_left : forall r, r < 0 -> Rabs r = - r.
Lemma Rabs_right : forall r, r >= 0 -> Rabs r = r.
Lemma Rabs_left1 : forall a:R, a <= 0 -> Rabs a = - a.
Lemma Rabs_pos : forall x:R, 0 <= Rabs x.
Lemma Rle_abs : forall x:R, x <= Rabs x.