Lemma Dcuts_max_open : Dcuts_def_open Dcuts_max_val. Proof. intros r ; apply hinhuniv ; apply sumofmaps ; [ intros Xr | intros Yr]. - generalize (X_open _ Xr). apply hinhfun ; intros q. exists (pr1 q) ; split. + apply hinhpr ; left. exact (pr1 (pr2 q)). + exact (pr2 (pr2 q)). - generalize (Y_open _ Yr). apply hinhfun ; intros q. exists (pr1 q) ; split. + apply hinhpr ; right. exact (pr1 (pr2 q)). + exact (pr2 (pr2 q)). 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.