`BookProof.GaussCoordCombo.gaussInt_coordCombo_sq` (i : Fin d) (c : ℕ → ℝ) (p K : ℕ) {R : MvPolynomial (Fin d) ℂ} (hR : pderiv i R = 0) : gaussInt (coordCombo i c p K * (coordCombo

Proved

BookProof.GaussCoordCombo.gaussInt_coordCombo_sq

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaussCoordCombo.

BookProof.GaussCoordCombo.gaussInt_coordCombo_sq (i : Fin d) (c : ℕ → ℝ) (p K : ℕ) {R : MvPolynomial (Fin d) ℂ} (hR : pderiv i R = 0) : gaussInt (coordCombo i c p K * (coordCombo i c p K * R)) = ((coordComboSum c p K : ℝ) : ℂ) * gaussInt R

Formalization note: Lean 4 identifier BookProof.GaussCoordCombo.gaussInt_coordCombo_sq.

Preamble

-- Generated from ChapterGaussCoordCombo.lean — theorem BookProof.GaussCoordCombo.gaussInt_coordCombo_sq
import Mathlib
import Definitions.Def_ChapterGaussCoordCombo
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.GaussCoordCombo



open MvPolynomial BookProof.HermiteProductCore

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.GaussCoordCombo.gaussInt_coordCombo_sq (i : Fin d) (c : ℕ → ℝ) (p K : ℕ)
    {R : MvPolynomial (Fin d) ℂ} (hR : pderiv i R = 0) :
    gaussInt (coordCombo i c p K * (coordCombo i c p K * R))
      = ((coordComboSum c p K : ℝ) : ℂ) * gaussInt R := by sorry

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