The Lean 4 theorem `re_gaussInt_kinPoly_self` in the `ChapterQgHermiteFriedrichs` chapter of the timepiece formalization

-- Generated from ChapterQgHermiteFriedrichs.lean — theorem BookProof.QgHermiteFriedrichs.re_gaussInt_kinPoly_self
import Mathlib
import Definitions.Def_ChapterQgHermiteFriedrichs
import Definitions.Def_ChapterSirkBandLedger
import Definitions.Def_ChapterRitzCertificate
open BookProof.QgHermiteFriedrichs







open MeasureTheory Complex MvPolynomial
open BookProof.HermiteProductCore BookProof.QgHermiteCore BookProof.Starobinsky
open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.FriedrichsExtension

noncomputable section

variable {d : ℕ}































variable (W : Vd d → ℝ)

theorem BookProof.QgHermiteFriedrichs.re_gaussInt_kinPoly_self (p : MvPolynomial (Fin d) ℂ) :
    (gaussInt (cpoly p * kinPoly p)).re = ∑ j : Fin d, ‖pgLp (coreD j p)‖ ^ 2 := by sorry