fact: Definition is_ideal (P : B → hProp) : hProp := ((∃ (b : B), P b) ∧ (∀ (a₁ a₂ : B), P a₁ ⇒ P a₂ ⇒ ∃ (b : B), P b ∧ a₁ ≺ b ∧ a₂ ≺ b) ∧ (∀ (a b : B), P b ⇒ a ≺ b ⇒ P a))%logic.
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 UniMath.OrderTheory.DCPOs.Basis.CompactBasis UniMath.OrderTheory.DCPOs.Elements.Maximal UniMath.OrderTheory.DCPOs.Examples.Products UniMath.OrderTheory.DCPOs.Examples.SubDCPO UniMath.OrderTheory.DCPOs.Examples.Propositions