Lemma NRNRtoR_mult : ∏ x x' y y' : NonnegativeReals, NRNRtoR (x * x' + y * y')%NR (x * y' + y * x')%NR = NRNRtoR x y * NRNRtoR x' y'. Proof. intros x x' y y'. apply pathsinv0, NR_to_hr_mult. 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.