∀ {R : Type u_2} {A : Type u_3} [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 : Subalgebra R A)
  (h : ∀ {a : A}, a ∈ S.carrier → star a ∈ S.carrier), ↑{ toSubalgebra := S, star_mem' := h } = ↑S