proposition: 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: Proof. exact (pr12 τ x 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