∀ {𝕜 : Type u_1} {E : Type u_2} {A : Type u_3} {B : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : CommSemiring A] {z : E} {s : Set E}
  [inst_4 : NormedRing B] [inst_5 : NormedAlgebra 𝕜 B] [inst_6 : Algebra A B] {f : E → B},
  AnalyticWithinAt 𝕜 f s z → ∀ (p : Polynomial A), AnalyticWithinAt 𝕜 (fun x => (Polynomial.aeval (f x)) p) s z