Lemma istrans_Dcuts_lt_rel : istrans Dcuts_lt_rel. Proof. intros x y z. apply hinhfun2. intros r n. exists (pr1 r) ; split. - exact (pr1 (pr2 r)). - apply is_Dcuts_bot with (pr1 n). + exact (pr2 (pr2 n)). + apply lt_leNonnegativeRationals. apply Dcuts_finite with y. * exact (pr1 (pr2 n)). * 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.