Lemma isirrefl_Dcuts_ap_rel : isirrefl Dcuts_ap_rel. Proof. intros x. unfold neg. apply sumofmaps. - now apply isirrefl_Dcuts_lt_rel. - now apply isirrefl_Dcuts_lt_rel. 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.