∀ {R : Type u_3} {A : Type u_4} {p p_1 : A → Prop} (e_p : p = p_1) [inst : CommSemiring R] [inst_1 : Nontrivial R]
  [inst_2 : StarRing R] [inst_3 : MetricSpace R] [inst_4 : IsTopologicalSemiring R] [inst_5 : ContinuousStar R]
  [inst_6 : NonUnitalRing A] [inst_7 : StarRing A] [inst_8 : TopologicalSpace A] [inst_9 : Module R A]
  [inst_10 : IsScalarTower R A A] [inst_11 : SMulCommClass R A A]
  [instCFCₙ : NonUnitalContinuousFunctionalCalculus R A p] (f f_1 : R → R),
  f = f_1 → ∀ (a a_1 : A), a = a_1 → cfcₙ f a = cfcₙ f_1 a_1