proposition: Lemma is_strongly_maximal_basis {X : dcpo} (B : dcpo_basis X) (x : X) : (∀ (i j : B), B i ≪ B j ⇒ (B i ≪ x ∨ is_hausdorff_separated (B j) x))%logic ≃ is_strongly_maximal x.
proof: Proof. use weqimplimpl. - apply is_strongly_maximal_basis_1. - apply is_strongly_maximal_basis_2. - apply propproperty. - apply propproperty. Qed.
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