∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {K : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} K]
  {C : Type u} [inst_2 : CategoryTheory.Category.{v, u} C] (F : CategoryTheory.Functor J C)
  [inst_3 : CategoryTheory.Limits.HasLimit F] (E : CategoryTheory.Functor K J)
  [inst_4 : CategoryTheory.Limits.HasLimit (E.comp F)] (k : K),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.limit.pre F E)
      (CategoryTheory.Limits.limit.π (E.comp F) k) =
    CategoryTheory.Limits.limit.π F (E.obj k)