(R : Type u_1) →
  (S : Type u_2) →
    (A : Type u_3) →
      (B : Type u_4) →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring S] →
            [inst_2 : Semiring A] →
              [inst_3 : Semiring B] →
                [inst_4 : Bialgebra S A] →
                  [inst_5 : Bialgebra R B] →
                    [inst_6 : Algebra R A] →
                      [inst_7 : Algebra R S] → [IsScalarTower R S A] → Bialgebra S (TensorProduct R A B)