Proposition indexed_functor_id {x : C} (xx : Φ x) : indexed_cat_id Ψ x (τ x xx) · indexed_functor_natural τ (identity x) xx = # (τ x) (indexed_cat_id Φ x xx). Proof. exact (pr12 τ x xx). 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.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategory.