∀ {J : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} J] {C : Type u_4}
  [inst_1 : CategoryTheory.Category.{u_3, u_4} C] {F : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cocone F)
  ⦃X Y : J⦄ (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      ((c.toCostructuredArrow.comp (CategoryTheory.CostructuredArrow.toOver F c.pt)).map f)
      (CategoryTheory.Over.homMk (c.ι.app Y) ⋯) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Over.homMk (c.ι.app X) ⋯)
      (((CategoryTheory.Functor.const J).obj (CategoryTheory.Over.mk (CategoryTheory.CategoryStruct.id c.pt))).map f)