∀ {J : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} J] (F : CategoryTheory.Functor J (Type u_3))
  (x : F.CoconeTypes) {j j' : J} (f : j ⟶ j'),
  CategoryTheory.CategoryStruct.comp (F.map f)
      ({ pt := x.pt, ι := { app := fun j => x.ι j, naturality := ⋯ } }.ι.app j') =
    { pt := x.pt, ι := { app := fun j => x.ι j, naturality := ⋯ } }.ι.app j