(R : Type u) →
  {A : Type v} →
    [inst : CommRing R] →
      [inst_1 : StarRing R] →
        [inst_2 : Ring A] →
          [inst_3 : Algebra R A] →
            [inst_4 : StarRing A] →
              [inst_5 : StarModule R A] →
                {s : Set A} →
                  (∀ a ∈ s, ∀ b ∈ s, a * b = b * a) →
                    (∀ a ∈ s, ∀ b ∈ s, a * star b = star b * a) → CommRing ↥(StarAlgebra.adjoin R s)