Lemma nat_to_NonnegativeReals_Sn : ∏ n : nat, nat_to_NonnegativeReals (S n) = nat_to_NonnegativeReals n + 1. Proof. intros n. unfold nat_to_NonnegativeReals. rewrite nat_to_NonnegativeRationals_Sn. rewrite NonnegativeRationals_to_NonnegativeReals_plus. 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.