Lemma Dcuts_mult_lecompat_l : ∏ x y z: Dcuts, (0 < x) -> (Dcuts_mult y x <= Dcuts_mult z x) -> (y <= z). Proof. intros x y z Hx0. intros H ; apply Dcuts_nlt_ge ; intro H0 ; apply (pr2 (Dcuts_nlt_ge _ _) H). 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.