proposition: 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: Proof. intros x Hap. rewrite ringcomm2. now apply (hr_islinv_neg x Hap). Qed.
imports: UniMath.Algebra.Groups UniMath.Foundations.Preamble UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.Sets UniMath.RealNumbers.NonnegativeRationals UniMath.RealNumbers.NonnegativeReals