Lemma NonnegativeRationals_to_Dcuts_bot (q : NonnegativeRationals) : Dcuts_def_bot (λ r : NonnegativeRationals, (r < q)%NRat). Proof. intros r Hr n Hnr. now apply istrans_le_lt_ltNonnegativeRationals with r. 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.