fact: Definition type_prod_pointwise_lub (i : I) : D i := ⨆ (app_directed_set_depfun E i).
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.PointedPosets UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous UniMath.OrderTheory.DCPOs.Examples.Propositions UniMath.OrderTheory.DCPOs.Examples.SubDCPO