∀ {J : Type u_3} [inst : CategoryTheory.Category.{u_1, u_3} J] {C : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_2, u_4} C] (F : CategoryTheory.Functor J C) {X Y : CategoryTheory.Limits.Cone F}
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id (CategoryTheory.Limits.Cone F)).map f)
      (CategoryTheory.Limits.Cones.eta Y).hom =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Cones.eta X).hom
      (((CategoryTheory.Limits.Cone.toCostructuredArrow F).comp
            (CategoryTheory.Limits.Cone.fromCostructuredArrow F)).map
        f)