Lemma Dcuts_min_carac_r : ∏ x y : Dcuts, y <= x -> Dcuts_min x y = y. Proof. intros x y Hxy. apply Dcuts_eq_is_eq ; intros r ; split. - intros Hr. exact (pr2 Hr). - intros Yr. split. + now simple refine (Hxy _ _). + exact Yr. 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.