Definition forall_Poset {X:UU} (P : X -> Poset) : Poset. Proof. use make_Poset. { exact (forall_hSet P). } use make_PartialOrder. { apply pointwiseorder. } apply ispartialorder_pointwiseorder. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.