Lemma isapfun_NonnegativeRationals_to_Dcuts' : ∏ q q' : NonnegativeRationals, q != q' → NonnegativeRationals_to_Dcuts q ≠ NonnegativeRationals_to_Dcuts q'. Proof. intros q q' H. apply noteq_ltorgtNonnegativeRationals in H. induction H as [H | H]. - now left ; apply (pr2 (isapfun_NonnegativeRationals_to_Dcuts_aux _ _)). - now right ; apply (pr2 (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.