Lemma Dcuts_plus_lecompat_l : ∏ x y z: Dcuts, (y <= z) <-> (Dcuts_plus y x <= Dcuts_plus z x). Proof. intros x y z. split. - intros H ; apply Dcuts_nlt_ge ; intro H0 ; apply (pr2 (Dcuts_nlt_ge _ _) H). now apply_pr2 (Dcuts_plus_ltcompat_l x). - intros H ; apply Dcuts_nlt_ge ; intro H0 ; apply (pr2 (Dcuts_nlt_ge _ _) H). now apply Dcuts_plus_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.