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

-- Generated from ChapterQuantumGravity3DGauge.lean — theorem BookProof.QuantumGravity3DGauge.coreRep_commutator
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_ChapterHermiteProductCore
import Definitions.Def_ChapterYangMillsHermite
open BookProof.HermiteProductCore
open BookProof.YangMillsHermite
open BookProof.QuantumGravity3DGauge

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



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

theorem BookProof.QuantumGravity3DGauge.coreRep_commutator {n m : ℕ} {kappa : Fin n → ℝ} (hk : ∀ i, 0 ≤ kappa i)
    (pi : Fin n → D →ₗ[ℂ] D) (Bf : Fin m → D →ₗ[ℂ] D) :
    signedOp kappa pi Bf
      = weylOp (fun i => ((Real.sqrt (kappa i) : ℝ) : ℂ) • pi i) Bf := by sorry