Lemma Dcuts_max_min : ∏ x y : Dcuts, Dcuts_max x (Dcuts_min x y) = x. Proof. intros x y. apply Dcuts_eq_is_eq ; intros r. split. - apply hinhuniv ; apply sumofmaps ; [intros Xr | intros Hr]. + exact Xr. + exact (pr1 Hr). - intros 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.