Definition is_z_iso_in_REL_to_unique_image {X Y : hSet} (r : bin_hrel X Y) : is_z_isomorphism (C := REL) r -> (∏ x: X, ∃! y : Y, r x y). Proof. intro i. intro x. exists (bin_hrel_is_z_iso_to_image i x). intro. apply (bin_hrel_is_z_iso_to_image_isaprop i x). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.All.