proposition: Lemma RtoNRNR_NRNRtoR : ∏ x y : NonnegativeReals, (RtoNRNR (NRNRtoR x y)) = ((x - y)%NR ,, (y - x)%NR).
proof: Proof. intros X Y. unfold RtoNRNR, NRNRtoR. unfold hr_to_NR, NR_to_hr. now rewrite setquotunivcomm. 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