proposition: Lemma nat_to_hr_O : nat_to_hr O = 0%ring.
proof: Proof. unfold nat_to_hr. rewrite nat_to_NonnegativeReals_O. 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