Lemma NonnegativeRationals_to_Dcuts_open (q : NonnegativeRationals) : Dcuts_def_open (λ r : NonnegativeRationals, (r < q)%NRat). Proof. intros r Hr. apply hinhpr. generalize (between_ltNonnegativeRationals r q Hr) ; intros n. exists (pr1 n). split. - exact (pr2 (pr2 n)). - exact (pr1 (pr2 n)). 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.