∀ (R : Type u_2) {A : Type u_1} [inst : CommRing R] [inst_1 : StarRing R] [inst_2 : Ring A] [inst_3 : Algebra R A]
  [inst_4 : StarRing A] [inst_5 : StarModule R A] {s : Set A} (n : ℕ) (a : ↥(StarAlgebra.adjoin R s).toSubalgebra),
  Ring.zsmul (↑n.succ) a = Ring.zsmul (↑n) a + a