∀ {X : Type u_1} {A : Type u_2} [inst : NonUnitalNormedRing A] [inst_1 : StarRing A] [inst_2 : NormedSpace ℝ A]
  [inst_3 : IsScalarTower ℝ A A] [inst_4 : SMulCommClass ℝ A A] [ContinuousStar A]
  [inst_6 : NonUnitalIsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_7 : PartialOrder A]
  [inst_8 : StarOrderedRing A] [inst_9 : NonnegSpectrumClass ℝ A] [T2Space A] [IsTopologicalRing A]
  [inst_12 : TopologicalSpace X] {s : Set NNReal},
  IsCompact s →
    ∀ (f : NNReal → NNReal) {a : X → A} {t : Set X},
      ContinuousOn a t →
        (∀ x ∈ t, quasispectrum NNReal (a x) ⊆ s) →
          (∀ x ∈ t, 0 ≤ a x) →
            autoParam (ContinuousOn f s) ContinuousOn.cfcₙ_nnreal'._auto_1 →
              autoParam (f 0 = 0) ContinuousOn.cfcₙ_nnreal'._auto_3 → ContinuousOn (fun x => cfcₙ f (a x)) t