`BookProof.GaussCoordCombo.pderiv_prod_eq_zero` {S : Finset (Fin d)} {W : Fin d → MvPolynomial (Fin d) ℂ} {i : Fin d} (h : ∀ j ∈ S, pderiv i (W j) = 0) : pderiv i (∏ j ∈ S, W j) =

Proved

BookProof.GaussCoordCombo.pderiv_prod_eq_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaussCoordCombo.

BookProof.GaussCoordCombo.pderiv_prod_eq_zero {S : Finset (Fin d)} {W : Fin d → MvPolynomial (Fin d) ℂ} {i : Fin d} (h : ∀ j ∈ S, pderiv i (W j) = 0) : pderiv i (∏ j ∈ S, W j) = 0

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

Preamble

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



open MvPolynomial BookProof.HermiteProductCore

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.GaussCoordCombo.pderiv_prod_eq_zero {S : Finset (Fin d)} {W : Fin d → MvPolynomial (Fin d) ℂ}
    {i : Fin d} (h : ∀ j ∈ S, pderiv i (W j) = 0) : pderiv i (∏ j ∈ S, W j) = 0 := by sorry

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