Lemma isaprop_Dcuts_ap_rel (X Y : Dcuts_set) : isaprop ((X < Y) ⨿ (Y < X)). Proof. apply (isapropcoprod (X < Y) (Y < X) (propproperty (X < Y)) (propproperty (Y < X)) (λ Hlt : X < Y, pr2 (Dcuts_le_ngt_rel Y X) (Dcuts_lt_le_rel X Y Hlt))). 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.