Lemma Dcuts_half_le : ∏ x : Dcuts, Dcuts_half x <= x. Proof. intros x. intros r Hr. apply is_Dcuts_bot with (1 := Hr). now apply plusNonnegativeRationals_le_l. 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.