∀ {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.Cocone F} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.id (CategoryTheory.Limits.Cocone F)).map f)
      ((fun c =>
            CategoryTheory.Limits.Cocones.ext
              (CategoryTheory.Iso.refl ((CategoryTheory.Functor.id (CategoryTheory.Limits.Cocone F)).obj c).pt) ⋯)
          Y).hom =
    CategoryTheory.CategoryStruct.comp
      ((fun c =>
            CategoryTheory.Limits.Cocones.ext
              (CategoryTheory.Iso.refl ((CategoryTheory.Functor.id (CategoryTheory.Limits.Cocone F)).obj c).pt) ⋯)
          X).hom
      (({ obj := fun c => Opposite.op c.op, map := fun {X Y} f => Quiver.Hom.op { hom := f.hom.op, w := ⋯ },
                map_id := ⋯, map_comp := ⋯ }.comp
            { obj := fun c => (Opposite.unop c).unop, map := fun {X Y} f => { hom := f.unop.hom.unop, w := ⋯ },
              map_id := ⋯, map_comp := ⋯ }).map
        f)