∀ {R : Type u_2} {A : Type u_1} [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 : IsSemitopologicalSemiring A] (s : StarSubalgebra R A) {a b : A},
  a ∈ s.topologicalClosure.carrier → b ∈ s.topologicalClosure.carrier → a + b ∈ s.topologicalClosure.carrier