∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : NonUnitalRing A] [inst_2 : StarRing A] [inst_3 : Module ℂ A]
  [inst_4 : IsScalarTower ℂ A A] [inst_5 : SMulCommClass ℂ A A] [T2Space A]
  [inst_7 : NonUnitalContinuousFunctionalCalculus ℂ A IsStarNormal] {a : A} (f : ℝ → ℝ),
  autoParam (IsSelfAdjoint a) cfcₙ_real_eq_complex._auto_1 → cfcₙ f a = cfcₙ (fun x => ↑(f x.re)) a