proposition: Lemma hr_to_NRneg_NR_to_hr : ∏ (x : NonnegativeReals × NonnegativeReals), hr_to_NRneg (NR_to_hr x) = pr2 x - pr1 x.
proof: Proof. intros x. unfold hr_to_NRneg, 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