proposition: Lemma isotoid_functorcat_pointwise (C : precategory_data) (D : category) (H : is_univalent D) (F G : ob [C, D, D]) (α: z_iso F G) (c: C) : toforallpaths (fun _ : ob C => ob D) (pr1 (pr1 F)) (pr1 (pr1 G)) (maponpaths pr1 (maponpaths pr1 (isotoid (functor_category C D) (is_univalent_functor_category C D H) α))) c = isotoid D H (functor_z_iso_pointwise_if_z_iso' C D F G α c).
proof: Proof. assert (aux := isotoid_functorcat_pointwise_aux C D H F G (isotoid (functor_category C D) (is_univalent_functor_category C D H) α)). rewrite (idtoiso_isotoid [C, D] _ ) in aux. apply aux. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core