Lemma maxNonnegativeReals_minus_plus: ∏ x y : NonnegativeReals, maxNonnegativeReals x y = (x - y) + y. Proof. intros x y. apply pathsinv0. now apply Dcuts_minus_plus_max. 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.