Lemma Dcuts_mult_ltcompat_r : ∏ x y z: Dcuts, (0 < x) -> (y < z) -> (Dcuts_mult x y < Dcuts_mult x z). Proof. intros x y z. rewrite ! (iscomm_Dcuts_mult x). now apply Dcuts_mult_ltcompat_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.