Lemma hr_opp_minus : ∏ x y : hr_commring, (x - y = - ((- x) - (- y)))%ring. Proof. intros x y. rewrite <- (hr_to_NR_bij x), <- (hr_to_NR_bij y). rewrite !NR_to_hr_opp, !NR_to_hr_plus, NR_to_hr_opp ; simpl. reflexivity. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.NonnegativeRationals.