`BookProof.HermiteExpWall.quadForm_scalaron_ge` (M alpha : ℝ) (hM : 0 < M) (halpha : 0 < alpha) (N : ℕ) : (M ^ 4 / (16 * alpha)) * ((8 * (Real.sqrt (2 / 3) / M) ^ 8 / 315) * (N : ℝ

Proved

BookProof.HermiteExpWall.quadForm_scalaron_ge

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.quadForm_scalaron_ge (M alpha : ℝ) (hM : 0 < M) (halpha : 0 < alpha) (N : ℕ) : (M ^ 4 / (16 * alpha)) * ((8 * (Real.sqrt (2 / 3) / M) ^ 8 / 315) * (N : ℝ) ^ 4 - 1) * gaussMoment (2 * N) ≤ ∫ x : ℝ, starobinskyV M alpha x * psi N x ^ 2

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

Preamble

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



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

noncomputable section

Formal statement

theorem BookProof.HermiteExpWall.quadForm_scalaron_ge (M alpha : ℝ) (hM : 0 < M) (halpha : 0 < alpha) (N : ℕ) :
    (M ^ 4 / (16 * alpha)) *
        ((8 * (Real.sqrt (2 / 3) / M) ^ 8 / 315) * (N : ℝ) ^ 4 - 1) * gaussMoment (2 * N)
      ≤ ∫ x : ℝ, starobinskyV M alpha x * psi N x ^ 2 := by sorry

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