Lemma NR_to_hr_minus : ∏ x y : NonnegativeReals × NonnegativeReals, (NR_to_hr x - NR_to_hr y)%ring = NR_to_hr (pr1 x + pr2 y ,, pr2 x + pr1 y). Proof. intros x y. rewrite NR_to_hr_opp, NR_to_hr_plus. 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.