∀ {R : Type uR} {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
  [inst_3 : CommSemiring B] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B] (r : A) (s : Set B)
  (B' : Subalgebra R B),
  r • s ⊆ ↑B' → ∀ {x : B}, x ∈ Algebra.adjoin R s → (algebraMap A B) r ∈ B' → ∃ n₀, ∀ n ≥ n₀, r ^ n • x ∈ B'