Lemma Dcuts_half_bot : Dcuts_def_bot Dcuts_half_val. Proof. intros r Hr q Hq. apply X_bot with (1 := Hr). eapply istrans_leNonnegativeRationals, plusNonnegativeRationals_lecompat_l, Hq. now apply plusNonnegativeRationals_lecompat_r, Hq. 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.