`BookProof.HermiteExpWall.gaussMoment_tilt_ge` (s : ℝ) (N : ℕ) : (s ^ 8 / 315) * gaussMoment (2 * N + 8) ≤ ∫ x : ℝ, Real.exp (-(2 * s) * x) * (x ^ (2 * N) * gaussW x)

Proved

BookProof.HermiteExpWall.gaussMoment_tilt_ge

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.gaussMoment_tilt_ge (s : ℝ) (N : ℕ) : (s ^ 8 / 315) * gaussMoment (2 * N + 8) ≤ ∫ x : ℝ, Real.exp (-(2 * s) * x) * (x ^ (2 * N) * gaussW x)

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

Preamble

-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.gaussMoment_tilt_ge
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterQgHermiteCore
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteCore
open BookProof.HermiteProductCore
open BookProof.HermiteExpWall



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

noncomputable section

Formal statement

theorem BookProof.HermiteExpWall.gaussMoment_tilt_ge (s : ℝ) (N : ℕ) :
    (s ^ 8 / 315) * gaussMoment (2 * N + 8)
      ≤ ∫ x : ℝ, Real.exp (-(2 * s) * x) * (x ^ (2 * N) * gaussW x) := by sorry

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