Lemma NonnegativeRationals_to_Dcuts_notin_le : ∏ (x : Dcuts) (r : NonnegativeRationals), ¬ (r ∈ x) -> x <= NonnegativeRationals_to_Dcuts r. Proof. intros x r Hr q Hq. simpl. now apply (Dcuts_finite x). 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.