Definition functor_z_iso_pointwise_if_z_iso' (C : precategory_data) (C' : category) (F G : ob [C, C']) (α: z_iso F G) : ∏ a : ob C, z_iso (pr1 F a) (pr1 G a) := λ a, tpair _ _ (is_functor_z_iso_pointwise_if_z_iso C C' _ F G (pr1 α) (pr2 α) a).
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Adjunctions.Core.