Lemma islabsorb_Dcuts_mult_zero : ∏ x : Dcuts, Dcuts_mult Dcuts_zero x = Dcuts_zero. Proof. intros x. apply Dcuts_eq_is_eq ; intro r ; split. - apply hinhuniv ; intros ix. apply fromempty. now apply (Dcuts_zero_empty _ (pr1 (pr2 (pr2 ix)))). - intro Hr. now apply Dcuts_zero_empty in Hr. 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.