∀ {R : Type u_1} {A : Type u_2} {p : A → Prop} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
  [inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : TopologicalSpace A] [inst_6 : Ring A]
  [inst_7 : StarRing A] [inst_8 : Algebra R A] [instCFC : ContinuousFunctionalCalculus R A p]
  [ContinuousMap.UniqueHom R A] (g f : R → R) (a : A),
  autoParam (ContinuousOn g (f '' spectrum R a)) cfc_comp'._auto_1 →
    autoParam (ContinuousOn f (spectrum R a)) cfc_comp'._auto_3 →
      autoParam (p a) cfc_comp'._auto_5 → cfc (fun x => g (f x)) a = cfc g (cfc f a)