proposition: Lemma NRNRtoR_lt : ∏ x x' y y' : NonnegativeReals, (x + y' < x' + y)%NR <-> NRNRtoR x y < NRNRtoR x' y'.
proof: Proof. intros x x' y y'. apply (NR_to_hr_lt (x,,y) (x' ,, y')). 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