Lemma Dcuts_max_carac_l : ∏ x y : Dcuts, y <= x -> Dcuts_max x y = x. Proof. intros x y Hxy. apply Dcuts_eq_is_eq ; intros r ; split. - apply hinhuniv ; apply sumofmaps ; [ intros Xr | intros Yr ]. + exact Xr. + now refine (Hxy _ _). - intros Xr. now apply hinhpr ; 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.