`BookProof.HermiteExpWall.l2_gaussPoly_le_of_gint_le` {q : Polynomial ℝ} {K : ℝ} (hK : 0 ≤ K) (N : ℕ) (h : gint (q * q) ≤ K ^ 2 * gaussMoment (2 * N)) : l2 (gaussPoly q) ≤ K * l2 (

Proved

BookProof.HermiteExpWall.l2_gaussPoly_le_of_gint_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHermiteExpWall.

BookProof.HermiteExpWall.l2_gaussPoly_le_of_gint_le {q : Polynomial ℝ} {K : ℝ} (hK : 0 ≤ K) (N : ℕ) (h : gint (q * q) ≤ K ^ 2 * gaussMoment (2 * N)) : l2 (gaussPoly q) ≤ K * l2 (psi N)

Formalization note: Lean 4 identifier BookProof.HermiteExpWall.l2_gaussPoly_le_of_gint_le.

Preamble

-- Generated from ChapterHermiteExpWall.lean — theorem BookProof.HermiteExpWall.l2_gaussPoly_le_of_gint_le
import Definitions.Def_ChapterStarobinskyPotential
import Mathlib
import Definitions.Def_ChapterHermiteExpWall
import Definitions.Def_ChapterGhostField
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterQgHermiteCore
open BookProof.GhostField
open BookProof.HermiteCore
open BookProof.HermiteProductCore
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.l2_gaussPoly_le_of_gint_le {q : Polynomial ℝ} {K : ℝ} (hK : 0 ≤ K) (N : ℕ)
    (h : gint (q * q) ≤ K ^ 2 * gaussMoment (2 * N)) :
    l2 (gaussPoly q) ≤ K * l2 (psi N) := by sorry

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