`BookProof.ScalaronFock.qgScalaronModeFock_deficiencyTrivialAt` {z : ℂ} (hz : z.im ≠ 0) : DeficiencyTrivialAt (modeFockCore a b M alpha Rc phi) (qgScalaronModeFockHamiltonian a b M

Proved

BookProof.ScalaronFock.qgScalaronModeFock_deficiencyTrivialAt

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalaronFockEsa.

BookProof.ScalaronFock.qgScalaronModeFock_deficiencyTrivialAt {z : ℂ} (hz : z.im ≠ 0) : DeficiencyTrivialAt (modeFockCore a b M alpha Rc phi) (qgScalaronModeFockHamiltonian a b M alpha Rc phi) z

Formalization note: Lean 4 identifier BookProof.ScalaronFock.qgScalaronModeFock_deficiencyTrivialAt.

Preamble

-- Generated from ChapterScalaronFockEsa.lean — theorem BookProof.ScalaronFock.qgScalaronModeFock_deficiencyTrivialAt
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterQuantumGravityDensitized
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterScalaronFockEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterScalaronCoreEsa
open BookProof.FarisLavine
open BookProof.ScalaronEsa
open BookProof.ScalaronFock


open Filter Topology MeasureTheory SchwartzMap


open BookProof.FarisLavine BookProof.Starobinsky BookProof.ScalaronEsa
open BookProof.DirectSumEsa BookProof.StoneBridge BookProof.EsaClosure
open BookProof.QuantumGravityDensitized BookProof.ChapterStoneResolvent

noncomputable section

variable {E : ℕ → Type*} [∀ n, NormedAddCommGroup (E n)] [∀ n, InnerProductSpace ℝ (E n)]
  [∀ n, FiniteDimensional ℝ (E n)] [∀ n, MeasurableSpace (E n)] [∀ n, BorelSpace (E n)]
variable (a b : ℕ → ℕ → ℝ) (M alpha : ℝ) (Rc phi : ℕ → ℕ → ℝ)

Formal statement

theorem BookProof.ScalaronFock.qgScalaronModeFock_deficiencyTrivialAt {z : ℂ} (hz : z.im ≠ 0) :
    DeficiencyTrivialAt (modeFockCore a b M alpha Rc phi)
      (qgScalaronModeFockHamiltonian a b M alpha Rc phi) z := by sorry

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