Lemma istight_Dcuts_ap_rel : istight Dcuts_ap_rel. Proof. intros X Y Hap. apply Dcuts_eq_is_eq. intros r ; split ; revert r. - change (X <= Y). apply Dcuts_le_ngt_rel. intro Hlt ; apply Hap. now right. - change (Y <= X). apply Dcuts_le_ngt_rel. intro Hlt ; apply Hap. now left. 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.