∀ {J : Type u_2} [inst : CategoryTheory.Category.{u_4, u_2} J] {C : Type u_3}
  [inst_1 : CategoryTheory.Category.{u_1, u_3} C] {F : CategoryTheory.Functor J C} {c c' : CategoryTheory.Limits.Cone F}
  (φ : c.pt ≅ c'.pt) (w : ∀ (j : J), c.π.app j = CategoryTheory.CategoryStruct.comp φ.hom (c'.π.app j)),
  CategoryTheory.CategoryStruct.comp { hom := φ.inv, w := ⋯ } { hom := φ.hom, w := ⋯ } =
    CategoryTheory.CategoryStruct.id c'