Prove2Me

`BookProof.GaussCoordCombo.hermiteFactor_succ_eq` (i : Fin d) (n : ℕ) : hermiteFactor i (n + 1) = X i * hermiteFactor i n - pderiv i (hermiteFactor i n)

Proved
BookProof.GaussCoordCombo.hermiteFactor_succ_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaussCoordCombo.

BookProof.GaussCoordCombo.hermiteFactor_succ_eq (i : Fin d) (n : ℕ) : hermiteFactor i (n + 1) = X i * hermiteFactor i n - pderiv i (hermiteFactor i n)

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

Preamble
-- Generated from ChapterGaussCoordCombo.lean — theorem BookProof.GaussCoordCombo.hermiteFactor_succ_eq
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.hermiteFactor_succ_eq (i : Fin d) (n : ℕ) :
    hermiteFactor i (n + 1) = X i * hermiteFactor i n - pderiv i (hermiteFactor i n) := by sorry

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