Lemma istight_apNonnegativeReals: ∏ x y : NonnegativeReals, (¬ (x ≠ y)) <-> (x = y). Proof. intros x y. split. - now apply istight_Dcuts_ap_rel. - intros ->. now apply isirrefl_Dcuts_ap_rel. 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.