Lemma iscotrans_Dcuts_ap_rel : iscotrans Dcuts_ap_rel. Proof. intros x y z. apply sumofmaps ; intros Hap. - generalize (iscotrans_Dcuts_lt_rel _ y _ Hap) ; apply hinhfun. apply sumofmaps ; intros Hy. + now left ; left. + now right ; left. - generalize (iscotrans_Dcuts_lt_rel _ y _ Hap) ; apply hinhfun. apply sumofmaps ; intros Hy. + now right ; right. + now left ; right. 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.