∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A] [inst_3 : PartialOrder A]
  [inst_4 : StarOrderedRing A] [inst_5 : IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint]
  [inst_6 : NonnegSpectrumClass ℝ A] [Nontrivial A] (f : NNReal → NNReal) (a : A),
  autoParam (ContinuousOn f (spectrum NNReal a)) IsGreatest.nnnorm_cfc_nnreal._auto_1 →
    autoParam (0 ≤ a) IsGreatest.nnnorm_cfc_nnreal._auto_3 → IsGreatest (f '' spectrum NNReal a) ‖cfc f a‖₊