The Lean 4 theorem `kinPoly_add_harmPoly_hermiteMv` in the `ChapterQgHermiteOscillatorEsa` chapter of the timepiece formalization

-- Generated from ChapterQgHermiteOscillatorEsa.lean — theorem BookProof.QgHermiteOscillator.kinPoly_add_harmPoly_hermiteMv
import Mathlib
import Definitions.Def_ChapterQgHermiteOscillatorEsa
open BookProof.QgHermiteOscillator











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

noncomputable section



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





variable {d : ℕ}

theorem BookProof.QgHermiteOscillator.kinPoly_add_harmPoly_hermiteMv (a : Fin d →₀ ℕ) :
    kinPoly (hermiteMv a) + harmPoly * hermiteMv a
      = (((mvDeg a : ℂ) + (d : ℂ) / 2)) • hermiteMv a := by sorry