Prove2Me

`BookProof.HermiteExpWall.integral_gaussPoly_sq` (q : Polynomial ℝ) : ∫ x : ℝ, gaussPoly q x ^ 2 = gint (q * q)

Proved
BookProof.HermiteExpWall.integral_gaussPoly_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.integral_gaussPoly_sq (q : Polynomial ℝ) : ∫ x : ℝ, gaussPoly q x ^ 2 = gint (q * q)

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

Preamble
-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.integral_gaussPoly_sq
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterHermiteProductCore
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterQgHermiteCore
open BookProof.HermiteCore
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.integral_gaussPoly_sq (q : Polynomial ℝ) :
    ∫ x : ℝ, gaussPoly q x ^ 2 = gint (q * q) := by sorry

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