∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : NonUnitalNonAssocRing A] [inst_2 : Module R A]
  [inst_3 : Star A] (S : NonUnitalStarSubalgebra R A),
  NonUnitalSubringClass.subtype S = ↑(NonUnitalStarSubalgebraClass.subtype S)