Lemma ap_ltNonnegativeReals : ∏ x y : NonnegativeReals, x ≠ y <-> (x < y) ⨿ (y < x). Proof. now intros x y ; split. 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.