proposition: Lemma hr_to_NR_one : hr_to_NR 1%ring = (1,,0).
proof: Proof. unfold ringunel2, unel_is ; simpl. unfold rigtoringunel2, hr_to_NR. rewrite setquotunivcomm ; simpl. erewrite <- minusNonnegativeReals_correct_r. - rewrite minusNonnegativeReals_eq_zero. + reflexivity. + apply isnonnegative_NonnegativeReals. - apply pathsinv0, isrunit_zero_plusNonnegativeReals. 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