Definition max := Rmax.
Definition min := Rmin.
Definition max_l := Rmax_l.
Definition max_r := Rmax_r.
Definition min_l := Rmin_l.
Definition min_r := Rmin_r.
End RHasMinMax.
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 opp_max_distr : forall n m : R, -(Rmax n m) = Rmin (- n) (- m).