∀ {R : Type u_2} {A : Type u_3} {p : A → Prop} [inst : CommSemiring R] [inst_1 : StarRing R] [inst_2 : MetricSpace R]
  [inst_3 : IsTopologicalSemiring R] [inst_4 : ContinuousStar R] [inst_5 : Ring A] [inst_6 : StarRing A]
  [inst_7 : MetricSpace A] [inst_8 : Algebra R A] [inst_9 : IsometricContinuousFunctionalCalculus R A p] (a : A)
  {s : Set R},
  spectrum R a ⊆ s →
    LipschitzOnWith 1 (fun f => cfc ((UniformOnFun.toFun {s}) f) a) {f | ContinuousOn ((UniformOnFun.toFun {s}) f) s}