proposition: Proposition is_ideal_rounded {P : B → hProp} (HP : is_ideal P) {a : B} (Ha : P a) : ∃ (b : B), a ≺ b ∧ P b.
proof: Proof. assert (H := is_ideal_top HP Ha Ha). revert H. use factor_through_squash. { apply propproperty. } intros b. induction b as ( b & p₁ & p₂ & p₃ ). exact (hinhpr (b ,, p₂ ,, p₁)). Qed.
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