proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Categories.HSET.All