Lemma inverse_swap_relation_iff {X Y : hSet} {r : bin_hrel X Y} (i : is_z_isomorphism (C := REL) r) : ∏ (x : X) (y : Y), r x y <-> pr1 i y x. Proof. intros x y. split. - exact (inverse_swap_relation i x y). - exact (inverse_swap_relation (pr2 (z_iso_inv ((r,,i) : z_iso (C := REL) _ _))) y x). Qed.
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.