{R : Type u_1} →
  {M : Type u_4} →
    {N : Type u_5} →
      [inst : Semiring R] →
        [inst_1 : AddMonoid M] →
          [inst_2 : AddMonoid N] → AddMonoidAlgebra R (M × N) ≃+* AddMonoidAlgebra (AddMonoidAlgebra R N) M