Lemma Dcuts_min_max : ∏ x y : Dcuts, Dcuts_min x (Dcuts_max x y) = x. Proof. intros x y. apply Dcuts_eq_is_eq ; intros r. split. - intros Hr. exact (pr1 Hr). - intros Xr. split. + exact Xr. + apply hinhpr. now left. 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.