`BookProof.YangMillsAbelianNoGap.gaussInt_one_eq` : gaussInt (1 : MvPolynomial (Fin d) ℂ) = (((Real.sqrt (2 * Real.pi)) ^ d : ℝ) : ℂ)

Proved

BookProof.YangMillsAbelianNoGap.gaussInt_one_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterYangMillsAbelianNoGap.

BookProof.YangMillsAbelianNoGap.gaussInt_one_eq : gaussInt (1 : MvPolynomial (Fin d) ℂ) = (((Real.sqrt (2 * Real.pi)) ^ d : ℝ) : ℂ)

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

Preamble

-- Generated from ChapterYangMillsAbelianNoGap.lean — theorem BookProof.YangMillsAbelianNoGap.gaussInt_one_eq
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterSqueezedGaussStates
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterYangMillsAbelianNoGap
import Definitions.Def_ChapterHermiteFunctions
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteCore
open BookProof.HermiteProductCore
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.gaussInt_one_eq :
    gaussInt (1 : MvPolynomial (Fin d) ℂ) = (((Real.sqrt (2 * Real.pi)) ^ d : ℝ) : ℂ) := by sorry

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