proposition: Lemma NR_to_hr_opp : ∏ x : NonnegativeReals × NonnegativeReals, (- NR_to_hr x)%ring = NR_to_hr (pr2 x ,, pr1 x).
proof: Proof. intros x. unfold ringinv1, grinv_is ; simpl. unfold abgrdiffinv. unfold NR_to_hr. apply (setquotfuncomm (binopeqrelabgrdiff (rigaddabmonoid NonnegativeReals)) (binopeqrelabgrdiff (rigaddabmonoid NonnegativeReals))). 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