proposition: Lemma Dcuts_notempty_notzero : ∏ (x : Dcuts) (r : NonnegativeRationals), r ∈ x -> x ≠ 0.
proof: Proof. intros x r Hx. right. apply hinhpr. exists r. split. - now apply Dcuts_zero_empty. - exact Hx. 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