∀ {R : Type u_2} {A : Type u_3} [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 T : StarSubalgebra R A} {x y : A},
  x ∈ S → y ∈ T → x * y ∈ S ⊔ T