Definition isupperbound_if_pointwise {X:UU} {P : X -> Poset} {I} {f : I -> forall_Poset P} {g : forall_Poset P} : isupperbound f g <-> forall x, isupperbound (fun i => f i x) (g x). Proof. split; intro H; repeat intro; use H. 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.