Prove2Me

`BookProof.YangMillsAbelianNoGap.gaussInt_bigP` : gaussInt (bigP vf Mf * bigP vf Mf) = (((∏ j, facS vf Mf j) * (Real.sqrt (2 * Real.pi)) ^ d : ℝ) : ℂ)

Proved
BookProof.YangMillsAbelianNoGap.gaussInt_bigP

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterYangMillsAbelianNoGap.

BookProof.YangMillsAbelianNoGap.gaussInt_bigP : gaussInt (bigP vf Mf * bigP vf Mf) = (((∏ j, facS vf Mf j) * (Real.sqrt (2 * Real.pi)) ^ d : ℝ) : ℂ)

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

Preamble
-- Generated from ChapterYangMillsAbelianNoGap.lean — theorem BookProof.YangMillsAbelianNoGap.gaussInt_bigP
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_ChapterHermiteProductCore
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}

variable (vf : Fin d → ℝ) (Mf : Fin d → ℕ)
Formal statement
theorem BookProof.YangMillsAbelianNoGap.gaussInt_bigP :
    gaussInt (bigP vf Mf * bigP vf Mf)
      = (((∏ j, facS vf Mf j) * (Real.sqrt (2 * Real.pi)) ^ d : ℝ) : ℂ) := by sorry

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