∀ {R : Type u_2} {A : Type u_1} {p : A → Prop} [inst : Semifield 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] [inst_9 : ContinuousFunctionalCalculus R A p] [ContinuousInv₀ R]
  (f : R → R) (a : A),
  (∀ x ∈ spectrum R a, f x ≠ 0) → ContinuousOn f (spectrum R a) → p a → cfc (fun x => (f x)⁻¹) a * cfc f a = 1