Lemma Dcuts_lt_le_rel : ∏ x y : Dcuts_set, Dcuts_lt_rel x y -> Dcuts_le_rel x y. Proof. intros x y ; apply hinhuniv ; intros r. intros n Xn. apply is_Dcuts_bot with (pr1 r). - exact (pr2 (pr2 r)). - apply lt_leNonnegativeRationals. apply Dcuts_finite with x. + exact (pr1 (pr2 r)). + exact Xn. 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.