Lemma Dcuts_plus_lecompat_r : ∏ x y z: Dcuts, (y <= z) <-> (Dcuts_plus x y <= Dcuts_plus x z). Proof. intros x y z. rewrite ! (iscomm_Dcuts_plus x). now apply Dcuts_plus_lecompat_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.