fact: Definition compact_basis_laws (B : dcpo_basis_data X) : UU := (∏ (b : B), is_compact_el (B b)) × (∏ (x : X), is_directed X (compact_basis_le_map B x)) × (∏ (x : X), is_least_upperbound X (compact_basis_le_map B x) x).
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous UniMath.OrderTheory.DCPOs.Core.WayBelow UniMath.OrderTheory.DCPOs.Basis.Continuous UniMath.OrderTheory.DCPOs.Basis.Algebraic UniMath.OrderTheory.DCPOs.Basis.Basis