Prove2Me

`BookProof.VielbeinFock.vielbeinFock_deficiencyTrivialAt` (M alpha : ℝ) (d : ℕ) (om : Fin d → ℝ) {z : ℂ} (hz : z.im ≠ 0) : DeficiencyTrivialAt (vielbeinFockCore d) (vielbeinFockHam

Proved
BookProof.VielbeinFock.vielbeinFock_deficiencyTrivialAt

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterVielbeinFiberFock.

BookProof.VielbeinFock.vielbeinFock_deficiencyTrivialAt (M alpha : ℝ) (d : ℕ) (om : Fin d → ℝ) {z : ℂ} (hz : z.im ≠ 0) : DeficiencyTrivialAt (vielbeinFockCore d) (vielbeinFockHamiltonian M alpha d om) z

Formalization note: Lean 4 identifier BookProof.VielbeinFock.vielbeinFock_deficiencyTrivialAt.

Preamble
-- Generated from ChapterVielbeinFiberFock.lean — theorem BookProof.VielbeinFock.vielbeinFock_deficiencyTrivialAt
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterScalaronCoreEsa
import Definitions.Def_ChapterScalaronFockEsa
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterVielbeinFiberFock
import Definitions.Def_ChapterFarisLavineCore
open BookProof.VielbeinFock


open Filter Topology MeasureTheory


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

noncomputable section
Formal statement
theorem BookProof.VielbeinFock.vielbeinFock_deficiencyTrivialAt (M alpha : ℝ) (d : ℕ) (om : Fin d → ℝ) {z : ℂ}
    (hz : z.im ≠ 0) :
    DeficiencyTrivialAt (vielbeinFockCore d) (vielbeinFockHamiltonian M alpha d om) z := by sorry

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