Prove2Me

`BookProof.QuantumGravityFock.qgGradedFock_essentiallySelfAdjointOn` (omega g : ℕ → ℝ) : EssentiallySelfAdjointOn (lpFiniteModes GradedIdx) ((lpFiniteModes GradedIdx).subtype.comp

Proved
BookProof.QuantumGravityFock.qgGradedFock_essentiallySelfAdjointOn

by leonardopedro · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityFock.

BookProof.QuantumGravityFock.qgGradedFock_essentiallySelfAdjointOn (omega g : ℕ → ℝ) : EssentiallySelfAdjointOn (lpFiniteModes GradedIdx) ((lpFiniteModes GradedIdx).subtype.comp (qgGradedHam omega g))

Formalization note: Lean 4 identifier BookProof.QuantumGravityFock.qgGradedFock_essentiallySelfAdjointOn.

Preamble
-- Generated from ChapterQuantumGravityFock.lean — theorem BookProof.QuantumGravityFock.qgGradedFock_essentiallySelfAdjointOn
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesFullEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Definitions.Def_ChapterFockSecondQuantization
import Mathlib
import Definitions.Def_ChapterQuantumGravityFock
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesFlow
open BookProof.QuantumGravityFock



open BookProof.NavierStokesFlow BookProof.NavierStokesFlow.IkebeKato
open BookProof.NavierStokesFlow.FockOfFock BookProof.NavierStokesFlow.FullEsa
open BookProof.FarisLavine BookProof.StoneBridge BookProof.EsaClosure
open BookProof.ChapterStoneResolvent BookProof.YangMillsFriedrichs
open BookProof.HermiteGalerkin BookProof.HashimotoShiftInvert
open BookProof.FockSecondQuantization

noncomputable section
Formal statement
theorem BookProof.QuantumGravityFock.qgGradedFock_essentiallySelfAdjointOn (omega g : ℕ → ℝ) :
    EssentiallySelfAdjointOn (lpFiniteModes GradedIdx)
      ((lpFiniteModes GradedIdx).subtype.comp (qgGradedHam omega g)) := by sorry

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