Definition unique_image_to_inverse_law_in_REL {X Y : hSet} {r : bin_hrel X Y} (py : (∏ y : Y, ∃! x : X, r x y)) (px : ∏ x: X, ∃! y : Y, r x y) (x1 x2 : X) : (∃ y : pr1 Y, r x1 y × r x2 y) = eqset x1 x2.
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.