proposition: Lemma NRNRtoR_zero : NRNRtoR 0%NR 0%NR = 0.
proof: Proof. unfold NRNRtoR, NR_to_hr. refine (setquotl0 _ 0 (_,,_)). apply hinhpr. exists 0%NR ; simpl. 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