Lemma istrans_Dcuts_le_lt_rel : ∏ x y z : Dcuts_set, Dcuts_le_rel x y -> Dcuts_lt_rel y z -> Dcuts_lt_rel x z. Proof. intros x y z Hle. apply hinhfun ; intros r. exists (pr1 r) ; split. - intros Xr ; apply (pr1 (pr2 r)). now refine (Hle _ _). - exact (pr2 (pr2 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.