Lemma hr_abs_opp : ∏ x : hr_ConstructiveField, hr_abs (- x)%ring = hr_abs x. Proof. intros x. unfold hr_abs. rewrite hr_to_NRpos_opp, hr_to_NRneg_opp. apply iscomm_maxNonnegativeReals. 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.