Lemma Dcuts_eq_is_eq : ∏ x y : Dcuts_set, Dcuts_eq x y -> x = y. Proof. intros x y Heq. apply subtypePath_prop. apply funextsec. intro r. apply hPropUnivalence. - exact (pr1 (Heq r)). - exact (pr2 (Heq r)). 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.