∀ {𝕜 : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} [inst : RCLike 𝕜] [inst_1 : NormedRing A]
  [inst_2 : StarRing A] [inst_3 : NormedAlgebra 𝕜 A] [inst_4 : IsometricContinuousFunctionalCalculus 𝕜 A p] (f : 𝕜 → 𝕜)
  (a : A) ⦃x : 𝕜⦄,
  x ∈ spectrum 𝕜 a →
    autoParam (ContinuousOn f (spectrum 𝕜 a)) norm_apply_le_norm_cfc._auto_1 →
      autoParam (p a) norm_apply_le_norm_cfc._auto_3 → ‖f x‖ ≤ ‖cfc f a‖