{ι : Type u_1} →
  {R : Type u_3} →
    {A : ι → Type u_4} →
      [inst : CommSemiring R] →
        [inst_1 : (i : ι) → Semiring (A i)] →
          [inst_2 : (i : ι) → Algebra R (A i)] →
            {S : Type u_5} →
              [inst_3 : Semiring S] →
                [inst_4 : Algebra R S] →
                  (f : MultilinearMap R A S) →
                    f 1 = 1 →
                      (∀ (x y : (i : ι) → A i), f (x * y) = f x * f y) → (PiTensorProduct R fun i => A i) →ₐ[R] S