Module R.
(** We obtain hence all the generic properties of max and min. *)
Include UsualMinMaxProperties R_as_OT RHasMinMax.
(** * Properties specific to the [R] domain *)
(** Compatibilities (consequences of monotonicity) *)
(** Anti-monotonicity swaps the role of [min] and [max] *)

Lemma minus_max_distr_l : forall n m p, Rmax (p - n) (p - m) = p - Rmin n m.