Definition is_least_upper_bound_pointwise {X:UU} {P : X -> Poset} {I} (f : I -> forall_Poset P) (g : forall_Poset P) : hProp := ∀ x, is_least_upper_bound (fun i => f i x) (g x).
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.