`BookProof.SecondQuantizationCore.essentiallySelfAdjointOn_fockSectorCore` (hcore : IsGraphCore D A) (n : ℕ) (hesa : EssentiallySelfAdjointOn (fockSectorDom Hs D₂ n) (fockSectorOp

Proved

BookProof.SecondQuantizationCore.essentiallySelfAdjointOn_fockSectorCore

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSecondQuantizationCoreEsa.

BookProof.SecondQuantizationCore.essentiallySelfAdjointOn_fockSectorCore (hcore : IsGraphCore D A) (n : ℕ) (hesa : EssentiallySelfAdjointOn (fockSectorDom Hs D₂ n) (fockSectorOp Hs D₂ A n)) : EssentiallySelfAdjointOn (fockSectorCore Hs D₂ D n) (restrictOp (fockSectorOp Hs D₂ A n) (fockSectorCore_le_fockSectorDom Hs D₂ D n))

Formalization note: Lean 4 identifier BookProof.SecondQuantizationCore.essentiallySelfAdjointOn_fockSectorCore.

Preamble

-- Generated from ChapterSecondQuantizationCoreEsa.lean — theorem BookProof.SecondQuantizationCore.essentiallySelfAdjointOn_fockSectorCore
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterDirectSumEsa
import Mathlib
import Definitions.Def_ChapterSecondQuantizationCoreEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterTensorGraphCore
open BookProof.GraphCore
open BookProof.TensorCore
open BookProof.SecondQuantizationCore



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore BookProof.TensorCore BookProof.DirectSumEsa

noncomputable section

variable (Hs : IPSpace) (D₂ : Submodule ℂ Hs.carrier) (A : D₂ →ₗ[ℂ] Hs.carrier)
  (D : Submodule ℂ Hs.carrier)

Formal statement

theorem BookProof.SecondQuantizationCore.essentiallySelfAdjointOn_fockSectorCore (hcore : IsGraphCore D A) (n : ℕ)
    (hesa : EssentiallySelfAdjointOn (fockSectorDom Hs D₂ n) (fockSectorOp Hs D₂ A n)) :
    EssentiallySelfAdjointOn (fockSectorCore Hs D₂ D n)
      (restrictOp (fockSectorOp Hs D₂ A n) (fockSectorCore_le_fockSectorDom Hs D₂ D n)) := by sorry

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