Lemma hr_to_NRneg_NR_to_hr : ∏ (x : NonnegativeReals × NonnegativeReals), hr_to_NRneg (NR_to_hr x) = pr2 x - pr1 x. Proof. intros x. unfold hr_to_NRneg, 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.