The Lean 4 theorem `torsionOps_symmetricOn` in the `ChapterQuantumGravity3DGauge` chapter of the timepiece formalization

-- Generated from ChapterQuantumGravity3DGauge.lean — theorem BookProof.QuantumGravity3DGauge.torsionOps_symmetricOn
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFriedrichsExtension
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Definitions.Def_ChapterComplexShiftCore
import Definitions.Def_ChapterQuantumGravityDensitized
import Mathlib
import Definitions.Def_ChapterQuantumGravity3DGauge
import Definitions.Def_ChapterF7
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterYangMillsHermite
open BookProof.ChapterF7
open BookProof.HermiteProductCore
open BookProof.YangMillsHermite
open BookProof.QuantumGravity3DGauge



open MeasureTheory Complex MvPolynomial Filter Topology
open BookProof.HermiteProductCore BookProof.YangMillsHermite BookProof.YangMillsFriedrichs
open BookProof.FarisLavine BookProof.FriedrichsExtension BookProof.HermiteGalerkin
open BookProof.HashimotoShiftInvert BookProof.QuantumGravityDensitized

noncomputable section

variable {d : ℕ}
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}
variable {D : Submodule ℂ (L2d 84)}

theorem BookProof.QuantumGravity3DGauge.torsionOps_symmetricOn
    (Φ : CoreRep 84 D) (m : Fin 64) :
    SymmetricOn D (D.subtype.comp (torsionOps Φ m)) := by sorry