Lemma isldistr_Dcuts_max_mult : isldistr Dcuts_max Dcuts_mult. Proof. intros x y z. apply Dcuts_eq_is_eq. intros r ; split. - apply hinhuniv. intros zxy. rewrite (pr1 (pr2 zxy)). generalize (pr2 (pr2 (pr2 zxy))). apply hinhfun. apply sumofmaps ; [intros Xr | intros Yr]. + left. apply hinhpr. exists (pr1 zxy). repeat split. * exact (pr1 (pr2 (pr2 zxy))). * exact Xr. + right. apply hinhpr. exists (pr1 zxy). repeat split. * exact (pr1 (pr2 (pr2 zxy))). * exact Yr. - apply hinhuniv. apply sumofmaps. + apply hinhfun. intros zx. rewrite (pr1 (pr2 zx)). exists (pr1 zx). repeat split. * exact (pr1 (pr2 (pr2 zx))). * apply hinhpr. left. exact (pr2 (pr2 (pr2 zx))). + apply hinhfun. intros zy. rewrite (pr1 (pr2 zy)). exists (pr1 zy). repeat split. * exact (pr1 (pr2 (pr2 zy))). * apply hinhpr. right. exact (pr2 (pr2 (pr2 zy))). 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.