`BookProof.YangMillsAbelianNoGap.norm_pgLp_sq` {q : MvPolynomial (Fin d) ℂ} (hq : RealCoeff q) {r : ℝ} (h : gaussInt (q * q) = ((r : ℝ) : ℂ)) : ‖pgLp q‖ ^ 2 = r

Proved

BookProof.YangMillsAbelianNoGap.norm_pgLp_sq

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterYangMillsAbelianNoGap.

BookProof.YangMillsAbelianNoGap.norm_pgLp_sq {q : MvPolynomial (Fin d) ℂ} (hq : RealCoeff q) {r : ℝ} (h : gaussInt (q * q) = ((r : ℝ) : ℂ)) : ‖pgLp q‖ ^ 2 = r

Formalization note: Lean 4 identifier BookProof.YangMillsAbelianNoGap.norm_pgLp_sq.

Preamble

-- Generated from ChapterYangMillsAbelianNoGap.lean — theorem BookProof.YangMillsAbelianNoGap.norm_pgLp_sq
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterSqueezedGaussStates
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterYangMillsAbelianNoGap
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterYangMillsHermite
open BookProof.HermiteProductCore
open BookProof.YangMillsHermite
open BookProof.YangMillsAbelianNoGap



open MvPolynomial MeasureTheory
open BookProof.HermiteProductCore BookProof.GaussCoordCombo BookProof.SqueezedGaussStates
open BookProof.YangMillsHermite BookProof.FarisLavine BookProof.HermiteGalerkin

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.YangMillsAbelianNoGap.norm_pgLp_sq {q : MvPolynomial (Fin d) ℂ} (hq : RealCoeff q) {r : ℝ}
    (h : gaussInt (q * q) = ((r : ℝ) : ℂ)) : ‖pgLp q‖ ^ 2 = r := by sorry

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