Lemma Dcuts_max_le : ∏ x y z, x <= z -> y <= z -> Dcuts_max x y <= z. Proof. intros x y z Hx Hy r. apply hinhuniv ; apply sumofmaps ; [intros Xr|intros Yr]. - now refine (Hx _ _). - now refine (Hy _ _). 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.