Lemma hr_isrinv_neg : ∏ (x : hr_commring) (Hap : hr_lt_rel x 0%ring), (x * NR_to_hr (0%NR,, invNonnegativeReals (hr_to_NRneg x) (pr2 (pr2 (hr_to_NR_negative _) Hap))))%ring = 1%ring. Proof. intros x Hap. rewrite ringcomm2. now apply (hr_islinv_neg x Hap). 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.