`BookProof.HermiteExpWall.gaussPolyDeriv_monomial` (m : ℕ) : gaussPolyDeriv ((Polynomial.X : Polynomial ℝ) ^ (m + 2)) = Polynomial.C ((m : ℝ) + 2) * Polynomial.X ^ (m + 1) - Polyno

Proved

BookProof.HermiteExpWall.gaussPolyDeriv_monomial

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.gaussPolyDeriv_monomial (m : ℕ) : gaussPolyDeriv ((Polynomial.X : Polynomial ℝ) ^ (m + 2)) = Polynomial.C ((m : ℝ) + 2) * Polynomial.X ^ (m + 1) - Polynomial.C (1 / 2 : ℝ) * Polynomial.X ^ (m + 3)

Formalization note: Lean 4 identifier BookProof.HermiteExpWall.gaussPolyDeriv_monomial.

Preamble

-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.gaussPolyDeriv_monomial
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterHermiteProductCore
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterQgHermiteCore
open BookProof.QgHermiteCore
open BookProof.HermiteExpWall



open MeasureTheory Polynomial
open BookProof.HermiteCore BookProof.Starobinsky BookProof.QgHermiteCore
open BookProof.HermiteProductCore

noncomputable section

Formal statement

theorem BookProof.HermiteExpWall.gaussPolyDeriv_monomial (m : ℕ) :
    gaussPolyDeriv ((Polynomial.X : Polynomial ℝ) ^ (m + 2))
      = Polynomial.C ((m : ℝ) + 2) * Polynomial.X ^ (m + 1)
        - Polynomial.C (1 / 2 : ℝ) * Polynomial.X ^ (m + 3) := by sorry

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