Lemma Dcuts_gt_nle : ∏ x y : Dcuts, x > y -> neg (x <= y). Proof. intros x y Hlt Hle. now apply (pr2 (Dcuts_le_ngt_rel _ _)) in Hle. 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.