proposition: Lemma nat_to_hr_S : ∏ n : nat, nat_to_hr (S n) = (1 + nat_to_hr n)%ring.
proof: Proof. intros n. unfold nat_to_hr. rewrite nat_to_NonnegativeReals_Sn, iscomm_plusNonnegativeReals. rewrite <- (hr_to_NR_bij 1%ring), hr_to_NR_one, NR_to_hr_plus. rewrite !isrunit_zero_plusNonnegativeReals. 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