∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u₃} [inst_1 : CategoryTheory.Category.{v₃, u₃} C]
  {F G : CategoryTheory.Functor J C} (c : CategoryTheory.Limits.Cone F) {d : CategoryTheory.Limits.Cone G}
  (hd : CategoryTheory.Limits.IsLimit d) (α : F ⟶ G) (j : J),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.IsLimit.map c hd α) (d.π.app j) =
    CategoryTheory.CategoryStruct.comp (c.π.app j) (α.app j)