∀ {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] {D : Type u_6} [inst_2 : CategoryTheory.Category.{u_5, u_6} D]
  {K : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cocone K) (F : CategoryTheory.Functor C D) {X : D}
  (f : F.obj c.pt ⟶ X) ⦃X_1 Y : J⦄ (f_1 : X_1 ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (((F.mapCocone c).toCostructuredArrow.comp
            ((CategoryTheory.CostructuredArrow.map f).comp (CategoryTheory.CostructuredArrow.pre K F X))).map
        f_1)
      (CategoryTheory.CostructuredArrow.homMk (c.ι.app Y) ⋯) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CostructuredArrow.homMk (c.ι.app X_1) ⋯)
      (((CategoryTheory.Functor.const J).obj (CategoryTheory.CostructuredArrow.mk f)).map f_1)