∀ {R : Type u_2} {A : Type u_1} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : Semiring A]
  [inst_3 : StarRing A] [inst_4 : Algebra R A] [inst_5 : StarModule R A] (S : StarSubalgebra R A) (x x_1 : ↥S),
  ↑(x * x_1) = ↑(x * x_1)