∀ {J : Type u_1} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J CategoryTheory.Cat)
  (s : CategoryTheory.Limits.Cone F) {X : ↑s.1} (j : J),
  CategoryTheory.Limits.limit.π (F.comp CategoryTheory.Cat.objects) j
      (CategoryTheory.Limits.limit.lift (F.comp CategoryTheory.Cat.objects)
        { pt := ↑s.pt, π := { app := fun j => (s.π.app j).toFunctor.obj, naturality := ⋯ } } X) =
    (s.π.app j).toFunctor.obj X