Lemma plusNonnegativeReals_eqcompat_r : ∏ x y z: NonnegativeReals, (x + y = x + z) <-> (y = z). Proof. intros x y z. rewrite ! (iscomm_plusNonnegativeReals x). now apply plusNonnegativeReals_eqcompat_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.