proposition: Proposition indexed_functor_comp {x y z : C} (f : x --> y) (g : y --> z) (xx : Φ x) : indexed_cat_comp Ψ f g (τ x xx) · indexed_functor_natural τ (f · g) xx = # (Ψ $ g) (indexed_functor_natural τ f xx) · (indexed_functor_natural τ g) ((Φ $ f) xx) · # (τ z) (indexed_cat_comp Φ f g xx).
proof: Proof. exact (pr22 τ x y z f g xx). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.IndexedCategories.IndexedCategory