Lemma NR_to_hr_plus : ∏ x y : NonnegativeReals × NonnegativeReals, (NR_to_hr x + NR_to_hr y)%ring = NR_to_hr (pr1 x + pr1 y ,, pr2 x + pr2 y). Proof. intros x y. unfold BinaryOperations.op1 ; simpl. unfold rigtoringop1 ; simpl. unfold NR_to_hr. apply (setquotfun2comm (binopeqrelabgrdiff (rigaddabmonoid NonnegativeReals)) (binopeqrelabgrdiff (rigaddabmonoid NonnegativeReals))). Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.NonnegativeRationals.