{R : Type u_1} →
  {A : Type u_2} →
    {p : A → Prop} →
      [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] →
                              {motive : NonUnitalContinuousFunctionalCalculus R A p → Sort u} →
                                (t : NonUnitalContinuousFunctionalCalculus R A p) →
                                  ((predicate_zero : p 0) →
                                      [compactSpace_quasispectrum : ∀ (a : A), CompactSpace ↑(quasispectrum R a)] →
                                        (exists_cfc_of_predicate :
                                            ∀ (a : A),
                                              p a →
                                                ∃ φ,
                                                  Continuous ⇑φ ∧
                                                    Function.Injective ⇑φ ∧
                                                      φ
                                                            {
                                                              toContinuousMap :=
                                                                ContinuousMap.restrict (quasispectrum R a)
                                                                  (ContinuousMap.id R),
                                                              map_zero' := ⋯ } =
                                                          a ∧
                                                        (∀ (f : ContinuousMapZero (↑(quasispectrum R a)) R),
                                                            quasispectrum R (φ f) = Set.range ⇑f) ∧
                                                          ∀ (f : ContinuousMapZero (↑(quasispectrum R a)) R), p (φ f)) →
                                          motive ⋯) →
                                    motive t