proposition: Lemma NR_to_hr_mult : ∏ x y : NonnegativeReals × NonnegativeReals, (NR_to_hr x * NR_to_hr y)%ring = NR_to_hr (pr1 x * pr1 y + pr2 x * pr2 y ,, pr1 x * pr2 y + pr2 x * pr1 y).
proof: Proof. intros x y. unfold BinaryOperations.op2 ; simpl. unfold rigtoringop2 ; simpl. unfold NR_to_hr. apply (setquotfun2comm (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