∀ {X : Type u_1} {𝕜 : Type u_2} {A : Type u_3} {p : A → Prop} [inst : RCLike 𝕜] [inst_1 : NormedRing A]
  [inst_2 : StarRing A] [inst_3 : NormedAlgebra 𝕜 A] [inst_4 : IsometricContinuousFunctionalCalculus 𝕜 A p]
  [ContinuousStar A] [inst_6 : TopologicalSpace X] {s : Set 𝕜},
  IsCompact s →
    ∀ (f : 𝕜 → 𝕜) {a : X → A},
      Continuous a →
        (∀ (x : X), spectrum 𝕜 (a x) ⊆ s) →
          autoParam (ContinuousOn f s) Continuous.cfc'._auto_1 →
            autoParam (∀ (x : X), p (a x)) Continuous.cfc'._auto_3 → Continuous fun x => cfc f (a x)