The Lean 4 theorem `momPoly_apply_prime` in the `ChapterHyperbolicQuadraticEsa` chapter of the timepiece formalization

-- Generated from ChapterHyperbolicQuadraticEsa.lean — theorem BookProof.HyperbolicQuadratic.momPoly_apply'
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Definitions.Def_ChapterNavierStokesDifferentialL2
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.HyperbolicQuadratic

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] {ι : Type*}
variable {d : ℕ}



open MeasureTheory MvPolynomial
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.FarisLavine
open BookProof.NavierStokesFlow.DifferentialL2

noncomputable section

theorem BookProof.HyperbolicQuadratic.momPoly_apply_prime (i : Fin d) (p : MvPolynomial (Fin d) ℂ) :
    momPoly i p = (-Complex.I) • (pderiv i p - (1/2 : ℂ) • (X i * p)) := by sorry