proposition: Lemma Dcuts_finite : ∏ X : Dcuts_set, ∏ r : NonnegativeRationals, neg (r ∈ X) -> ∏ n : NonnegativeRationals, n ∈ X -> n < r.
proof: Proof. intros X r Hr n Hn. apply notge_ltNonnegativeRationals ; intro Hn'. apply Hr. apply is_Dcuts_bot with n. - exact Hn. - exact Hn'. 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