∀ {X : Type u_1} {A : Type u_2} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A]
  [inst_3 : IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [ContinuousStar A] [inst_5 : PartialOrder A]
  [inst_6 : StarOrderedRing A] [inst_7 : NonnegSpectrumClass ℝ A] [T2Space A] [IsSemitopologicalRing A]
  [CompleteSpace A] [inst_11 : TopologicalSpace X] {s : Set NNReal} (f : NNReal → NNReal) {a : X → A},
  s ∈ nhdsSet (⋃ x, spectrum NNReal (a x)) →
    Continuous a →
      autoParam (∀ (x : X), 0 ≤ a x) Continuous.cfc_nnreal_of_mem_nhdsSet._auto_1 →
        autoParam (ContinuousOn f s) Continuous.cfc_nnreal_of_mem_nhdsSet._auto_3 → Continuous fun x => cfc f (a x)