{R : Type u_5} →
  [inst : CommSemiring R] →
    {A : Type u_6} →
      [inst_1 : Semiring A] →
        [inst_2 : Algebra R A] →
          {ι : Type u_7} →
            [inst_3 : DecidableEq ι] →
              [inst_4 : AddMonoid ι] →
                {M : ι → Submodule R A} → [SetLike.GradedMonoid M] → DirectSum.IsInternal M → GradedAlgebra M