Lemma Dcuts_NQmult_open : Dcuts_def_open Dcuts_NQmult_val. Proof. intros r. apply hinhuniv ; intros ry. generalize (Y_open _ (pr2 (pr2 ry))). apply hinhfun. intros ny. exists (x * pr1 ny). split. - apply hinhpr ; exists (pr1 ny). split. + reflexivity. + exact (pr1 (pr2 ny)). - pattern r at 1 ; rewrite (pr1 (pr2 ry)). apply multNonnegativeRationals_ltcompat_l. + exact Hx. + exact (pr2 (pr2 ny)). 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.