Lemma Dcuts_minus_le : ∏ x y, Dcuts_minus x y <= x. Proof. intros X Y r. apply hinhuniv ; intros x. apply is_Dcuts_bot with (1 := pr1 (pr2 x)). apply lt_leNonnegativeRationals. pattern r at 1 ; rewrite <- (isrunit_zeroNonnegativeRationals r). apply (pr2 (pr2 x)). now right. 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.