proposition: Lemma hr_to_NR_zero : hr_to_NR 0%ring = (0,,0).
proof: Proof. unfold ringunel1, unel_is ; simpl. unfold hr_to_NR. rewrite setquotunivcomm ; simpl. rewrite !minusNonnegativeReals_eq_zero. { reflexivity. } apply isrefl_leNonnegativeReals. 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