Lemma NonnegativeRationals_to_NonnegativeReals_nattorig : ∏ n : nat, NonnegativeRationals_to_NonnegativeReals (nattorig n) = nattorig n. Proof. induction n as [|n IHn]. - reflexivity. - rewrite !nattorigS. rewrite NonnegativeRationals_to_NonnegativeReals_plus, IHn. reflexivity. Qed.
Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.NonnegativeRationals.