∀ {J : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  {F : CategoryTheory.Functor J C} [inst_2 : CategoryTheory.Limits.HasLimit F] {X : C}
  {f f' : X ⟶ CategoryTheory.Limits.limit F},
  f = f' ↔
    ∀ (j : J),
      CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.limit.π F j) =
        CategoryTheory.CategoryStruct.comp f' (CategoryTheory.Limits.limit.π F j)