Definition directed_complete_depfunction : directed_complete_poset (depfunction_poset (λ i, D i) (λ i, D i)). Proof. intros J E HE. use make_lub. - exact (type_prod_pointwise_lub (J ,, (E ,, HE))). - exact (is_lub_type_prod_pointwise_lub (J ,, (E ,, HE))). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.PointedPosets. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions. 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.Examples.Propositions. Require Import UniMath.OrderTheory.DCPOs.Examples.SubDCPO.