Definition is_ideal_lower_set {P : B → hProp} (HP : is_ideal P) {a b : B} (Hb : P b) (p : a ≺ b) : P a := pr22 HP a b Hb p.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.OrderTheory.DCPOs.Core.DirectedSets. Require Import UniMath.OrderTheory.DCPOs.Core.Basics. Require Import UniMath.OrderTheory.DCPOs.Core.ScottContinuous. Require Import UniMath.OrderTheory.DCPOs.Core.WayBelow. Require Import UniMath.OrderTheory.DCPOs.Basis.Continuous. Require Import UniMath.OrderTheory.DCPOs.Basis.Algebraic. Require Import UniMath.OrderTheory.DCPOs.Basis.Basis. Require Import UniMath.OrderTheory.DCPOs.Basis.CompactBasis. Require Import UniMath.OrderTheory.DCPOs.Elements.Maximal. Require Import UniMath.OrderTheory.DCPOs.Examples.Products. Require Import UniMath.OrderTheory.DCPOs.Examples.SubDCPO. Require Import UniMath.OrderTheory.DCPOs.Examples.Propositions.