{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : StarRing R] →
        [inst_2 : TopologicalSpace A] →
          [inst_3 : Semiring A] →
            [inst_4 : Algebra R A] →
              [inst_5 : StarRing A] →
                [inst_6 : StarModule R A] →
                  [inst_7 : IsTopologicalSemiring A] →
                    [inst_8 : ContinuousStar A] →
                      [T2Space A] →
                        (s : StarSubalgebra R A) → (∀ (x y : ↥s), x * y = y * x) → CommSemiring ↥s.topologicalClosure