Lemma bin_hrel_z_iso_equiv_hset_z_iso_law {X Y : hSet} (i : z_iso (C := HSET) X Y) : bin_hrel_is_z_iso_to_function (invertiblefunction_to_invertiblerelation (pr2 i)) = pr1 i. Proof. apply funextsec ; intro x. exact (base_paths _ _ (pr1 (bin_hrel_is_z_iso_to_image_isaprop (invertiblefunction_to_invertiblerelation (pr2 i)) x (bin_hrel_is_z_iso_to_image (invertiblefunction_to_invertiblerelation (pr2 i)) x) (pr1 i x ,, idpath _)))). 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.