`BookProof.SecondQuantizationCore.symmetricOn_dGammaCoreOp` (hA : SymmetricOn D₂ A) : SymmetricOn (dsCore (fun n : ℕ => fockSectorCore Hs D₂ D n)) (dGammaCoreOp Hs D₂ A D)

Proved

BookProof.SecondQuantizationCore.symmetricOn_dGammaCoreOp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSecondQuantizationCoreEsa.

BookProof.SecondQuantizationCore.symmetricOn_dGammaCoreOp (hA : SymmetricOn D₂ A) : SymmetricOn (dsCore (fun n : ℕ => fockSectorCore Hs D₂ D n)) (dGammaCoreOp Hs D₂ A D)

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

Preamble

-- Generated from ChapterSecondQuantizationCoreEsa.lean — theorem BookProof.SecondQuantizationCore.symmetricOn_dGammaCoreOp
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterSecondQuantizationCoreEsa
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterTensorGraphCore
open BookProof.DirectSumEsa
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.symmetricOn_dGammaCoreOp (hA : SymmetricOn D₂ A) :
    SymmetricOn (dsCore (fun n : ℕ => fockSectorCore Hs D₂ D n)) (dGammaCoreOp Hs D₂ A D) := by sorry

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