∀ {R : Type u_2} {A : Type u_1} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : NonUnitalSemiring A]
  [inst_3 : StarRing A] [inst_4 : Module R A] [inst_5 : StarModule R A] (S : NonUnitalSubalgebra R A) (r : R),
  ∀ x ∈ star { carrier := star S.carrier, add_mem' := ⋯, zero_mem' := ⋯, mul_mem' := ⋯, smul_mem' := ⋯ }.carrier,
    r • x ∈ star { carrier := star S.carrier, add_mem' := ⋯, zero_mem' := ⋯, mul_mem' := ⋯, smul_mem' := ⋯ }.carrier