Definition inv_comma : y --> x. Proof. refine ((inv_from_z_iso (make_z_iso' _ Hf1) ,, inv_from_z_iso (make_z_iso' _ Hf2)) ,, _). abstract (cbn; apply pathsinv0; rewrite !functor_on_inv_from_z_iso; use z_iso_inv_on_left; rewrite assoc'; refine (!_) ; use z_iso_inv_on_right; cbn; exact (pr2 f)). 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.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering.