Lemma plusNonnegativeReals_apcompat_r : ∏ x y z: NonnegativeReals, (y ≠ z) <-> (x + y ≠ x + z). Proof. intros x y z. rewrite ! (iscomm_plusNonnegativeReals x). now apply plusNonnegativeReals_apcompat_l. 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.