Definition below_ideal_directed_set (I : rounded_ideal_completion) : directed_set rounded_ideal_completion. Proof. use make_directed_set. - exact (∑ (b : B), b ∈ I). - exact (λ b, principal_ideal (pr1 b)). - exact (is_directed_below_ideal I). Defined.
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.