Definition image_carrier_univ {X Y : UU} (f : X -> Y) (A : hsubtype Y ) : (∀ x:X, A (f x)) <-> (∀ y : image f, A (pr1 y)). Proof. split. - intros H [y im_y]. eapply image_univ'; eassumption. - intros H; cbn. apply image_univ'. intros y im_y. exact (H (y,,im_y)). 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.