∀ {R : Type u_1} {A : Type u_2} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
  [inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : StarModule R A] (S : Subalgebra R A),
  {
      carrier :=
        star
          { carrier := star S.carrier, mul_mem' := ⋯, one_mem' := ⋯, add_mem' := ⋯, zero_mem' := ⋯,
              algebraMap_mem' := ⋯ }.carrier,
      mul_mem' := ⋯, one_mem' := ⋯, add_mem' := ⋯, zero_mem' := ⋯, algebraMap_mem' := ⋯ } =
    S