Lemma Dcuts_mult_open : Dcuts_def_open Dcuts_mult_val. Proof. intros r. apply hinhuniv ; intros xy. generalize (X_open _ (pr1 (pr2 (pr2 xy)))) (Y_open _ (pr2 (pr2 (pr2 xy)))). apply hinhfun2. intros nx ny. exists (pr1 nx * pr1 ny). split. - apply hinhpr ; exists (pr1 nx ,, pr1 ny). repeat split. + exact (pr1 (pr2 nx)). + exact (pr1 (pr2 ny)). - pattern r at 1 ; rewrite (pr1 (pr2 xy)). apply multNonnegativeRationals_ltcompat. + exact (pr2 (pr2 nx)). + 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.