Definition depfunction_pointed_poset {X : UU} (Y : X → hSet) (RY : ∏ (x : X), pointed_PartialOrder (Y x)) : pointed_PartialOrder (forall_hSet Y). Proof. use make_pointed_PartialOrder. - exact (depfunction_poset Y RY). - exact (λ x, ⊥_{RY x}). - intros y x. apply pointed_PartialOrder_min_point. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets.Basics. Require Import UniMath.OrderTheory.Posets.MonotoneFunctions.