proposition: Lemma NR_to_hr_minus : ∏ x y : NonnegativeReals × NonnegativeReals, (NR_to_hr x - NR_to_hr y)%ring = NR_to_hr (pr1 x + pr2 y ,, pr2 x + pr1 y).
proof: Proof. intros x y. rewrite NR_to_hr_opp, NR_to_hr_plus. reflexivity. 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