`BookProof.GaussCoordCombo.gaussInt_hermiteFactor_mul` (i : Fin d) (m n : ℕ) {R : MvPolynomial (Fin d) ℂ} (hR : pderiv i R = 0) : gaussInt (hermiteFactor i m * (hermiteFactor i n *

Proved

BookProof.GaussCoordCombo.gaussInt_hermiteFactor_mul

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaussCoordCombo.

BookProof.GaussCoordCombo.gaussInt_hermiteFactor_mul (i : Fin d) (m n : ℕ) {R : MvPolynomial (Fin d) ℂ} (hR : pderiv i R = 0) : gaussInt (hermiteFactor i m * (hermiteFactor i n * R)) = (if m = n then (n.factorial : ℂ) else 0) * gaussInt R

Formalization note: Lean 4 identifier BookProof.GaussCoordCombo.gaussInt_hermiteFactor_mul.

Preamble

-- Generated from ChapterGaussCoordCombo.lean — theorem BookProof.GaussCoordCombo.gaussInt_hermiteFactor_mul
import Mathlib
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.GaussCoordCombo



open MvPolynomial BookProof.HermiteProductCore

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.GaussCoordCombo.gaussInt_hermiteFactor_mul (i : Fin d) (m n : ℕ) {R : MvPolynomial (Fin d) ℂ}
    (hR : pderiv i R = 0) :
    gaussInt (hermiteFactor i m * (hermiteFactor i n * R))
      = (if m = n then (n.factorial : ℂ) else 0) * gaussInt R := by sorry

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