The Lean 4 theorem `gaussInt_cross` in the `ChapterHermiteQuadraticEsa` chapter of the timepiece formalization

-- Generated from ChapterHermiteQuadraticEsa.lean — theorem BookProof.HermiteQuadraticEsa.gaussInt_cross
import Mathlib
import Definitions.Def_ChapterHermiteQuadraticEsa
open BookProof.HermiteQuadraticEsa














open MeasureTheory Complex MvPolynomial
open BookProof.HermiteProductCore BookProof.QgHermiteCore BookProof.QgHermiteFriedrichs
open BookProof.QgHermiteOscillator BookProof.FarisLavine BookProof.Starobinsky
open BookProof.StoneBridge BookProof.EsaClosure BookProof.ChapterStoneResolvent

noncomputable section

variable {d : ℕ}

theorem BookProof.HermiteQuadraticEsa.gaussInt_cross (j : Fin d) (p : MvPolynomial (Fin d) ℂ) :
    gaussInt (cpoly (coreD j p) * (X j * p)) + gaussInt (cpoly p * (X j * coreD j p))
      = -gaussInt (cpoly p * p) := by sorry