Lemma Dcuts_max_bot : Dcuts_def_bot Dcuts_max_val. Proof. intros r Hr q Hqr. revert Hr ; apply hinhfun ; apply sumofmaps ; [ intros Xr| intros Yr]. - left ; now apply X_bot with (1 := Xr). - right ; now apply Y_bot with (1 := Yr). 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.