proposition: Lemma isapfun_NonnegativeRationals_to_Dcuts : ∏ q q' : NonnegativeRationals, NonnegativeRationals_to_Dcuts q ≠ NonnegativeRationals_to_Dcuts q' → q != q'.
proof: 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.
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