Lemma Dcuts_max_carac_r : ∏ x y : Dcuts, x <= y -> Dcuts_max x y = y. Proof. intros x y Hxy. rewrite iscomm_Dcuts_max. now apply Dcuts_max_carac_l. Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.