fact: Definition to_hausdorff_separated_continuous_dcpo {X : dcpo} (B : dcpo_basis X) (x y : X) : (∃ (b₁ b₂ : B), B b₁ ≪ x ∧ B b₂ ≪ y ∧ ¬(∃ (t : B), B b₁ ≪ B t ∧ B b₂ ≪ B t))%logic → is_hausdorff_separated x y.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.WayBelow UniMath.OrderTheory.DCPOs.Core.ScottTopology UniMath.OrderTheory.DCPOs.Core.IntrinsicApartness UniMath.OrderTheory.DCPOs.Basis.Continuous UniMath.OrderTheory.DCPOs.Basis.Basis UniMath.OrderTheory.DCPOs.Elements.Sharp