∀ {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.Cocone F} (φ : c.pt ≅ c'.pt)
  (w : ∀ (j : J), CategoryTheory.CategoryStruct.comp (c.ι.app j) φ.hom = c'.ι.app j),
  CategoryTheory.CategoryStruct.comp { hom := φ.inv, w := ⋯ } { hom := φ.hom, w := ⋯ } =
    CategoryTheory.CategoryStruct.id c'