∀ {𝕜 : Type u_1} {A : Type u_2} {p : outParam (A → Prop)} [inst : RCLike 𝕜] [inst_1 : NonUnitalNormedRing A]
  [inst_2 : StarRing A] [inst_3 : NormedSpace 𝕜 A] [inst_4 : IsScalarTower 𝕜 A A] [inst_5 : SMulCommClass 𝕜 A A]
  [inst_6 : NonUnitalIsometricContinuousFunctionalCalculus 𝕜 A p] (f : 𝕜 → 𝕜) (a : A) (c : ℝ),
  autoParam (ContinuousOn f (quasispectrum 𝕜 a)) norm_cfcₙ_lt_iff._auto_1 →
    autoParam (f 0 = 0) norm_cfcₙ_lt_iff._auto_3 →
      autoParam (p a) norm_cfcₙ_lt_iff._auto_5 → (‖cfcₙ f a‖ < c ↔ ∀ x ∈ quasispectrum 𝕜 a, ‖f x‖ < c)