proposition: Lemma isapfun_NonnegativeRationals_to_Dcuts' : ∏ q q' : NonnegativeRationals, q != q' → NonnegativeRationals_to_Dcuts q ≠ NonnegativeRationals_to_Dcuts q'.
proof: 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.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.RealNumbers.Sets UniMath.Algebra.ConstructiveStructures UniMath.OrderTheory.Lattice.Lattice UniMath.RealNumbers.Prelim UniMath.RealNumbers.NonnegativeRationals