Lemma iscomm_minusNonnegativeReals : ∏ x y z : NonnegativeReals, x - y - z = x - z - y. Proof. intros x y z. rewrite !isassoc_minusNonnegativeReals. apply maponpaths. now apply iscomm_plusNonnegativeReals. 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.