Proposition indexed_nat_trans_natural {C : category} {Φ Ψ : indexed_cat C} {τ θ : indexed_functor Φ Ψ} (m : indexed_nat_trans τ θ) {x y : C} (f : x --> y) (xx : Φ x) : indexed_functor_natural τ f xx · m y ((Φ $ f) xx) = # (Ψ $ f) (m x xx) · indexed_functor_natural θ f xx. Proof. exact (pr2 m x y f 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. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedFunctor.