Lemma isapfun_NonnegativeRationals_to_Dcuts : ∏ q q' : NonnegativeRationals, NonnegativeRationals_to_Dcuts q ≠ NonnegativeRationals_to_Dcuts q' → q != q'. Proof. intros q q'. apply sumofmaps ; intros Hap. - now apply ltNonnegativeRationals_noteq, isapfun_NonnegativeRationals_to_Dcuts_aux. - now apply gtNonnegativeRationals_noteq, isapfun_NonnegativeRationals_to_Dcuts_aux. 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.