Lemma hr_to_NRpos_opp : ∏ x : hr_commring, hr_to_NRpos (- x)%ring = hr_to_NRneg x. Proof. intros x. unfold hr_to_NRpos. now rewrite hr_to_NR_opp. 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.