{R : Type u_1} →
  {A : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : TopologicalSpace A] →
        [inst_2 : Star A] →
          [inst_3 : NonUnitalSemiring A] →
            [inst_4 : Module R A] →
              [inst_5 : IsTopologicalSemiring A] →
                [inst_6 : ContinuousStar A] →
                  [inst_7 : ContinuousConstSMul R A] →
                    [T2Space A] →
                      (s : NonUnitalStarSubalgebra R A) →
                        (∀ (x y : ↥s), x * y = y * x) → NonUnitalCommSemiring ↥s.topologicalClosure