Lemma Dcuts_notempty_notzero : ∏ (x : Dcuts) (r : NonnegativeRationals), r ∈ x -> x ≠ 0. Proof. intros x r Hx. right. apply hinhpr. exists r. split. - now apply Dcuts_zero_empty. - exact Hx. 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.