Lemma hr_to_NRpos_NR_to_hr : ∏ (x : NonnegativeReals × NonnegativeReals), hr_to_NRpos (NR_to_hr x) = pr1 x - pr2 x. Proof. intros x. unfold hr_to_NRpos, hr_to_NR, NR_to_hr. now rewrite setquotunivcomm. 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.