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`BookProof.FullQuadratic.fqOp_symmetric` (P Q S : Fin d → Fin d → ℝ) (b b' : Fin d → ℝ) : SymmetricOn (polyGaussCore (d := d)) (fqOp P Q S b b')

Proved
BookProof.FullQuadratic.fqOp_symmetric

by leonardopedro · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFullQuadraticEsa.

BookProof.FullQuadratic.fqOp_symmetric (P Q S : Fin d → Fin d → ℝ) (b b' : Fin d → ℝ) : SymmetricOn (polyGaussCore (d := d)) (fqOp P Q S b b')

Formalization note: Lean 4 identifier BookProof.FullQuadratic.fqOp_symmetric.

Preamble
-- Generated from ChapterFullQuadraticEsa.lean — theorem BookProof.FullQuadratic.fqOp_symmetric
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterHermiteRelativeBound
import Definitions.Def_ChapterQuadratureEsa
import Definitions.Def_ChapterCarlemanTwoStep
import Definitions.Def_ChapterCarlemanSimplex
import Definitions.Def_ChapterModeQuadraticEsa
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterFullQuadraticEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterGaussCoreQuadBounds
open BookProof.HermiteProductCore
open BookProof.FullQuadratic



open Finset MeasureTheory MvPolynomial
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.FarisLavine
open BookProof.HyperbolicQuadratic
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.HermiteRelative
open BookProof.QuadratureEsa
open BookProof.StoneBridge BookProof.EsaClosure BookProof.ChapterStoneResolvent

noncomputable section

variable {d : ℕ}
Formal statement
theorem BookProof.FullQuadratic.fqOp_symmetric (P Q S : Fin d → Fin d → ℝ) (b b' : Fin d → ℝ) :
    SymmetricOn (polyGaussCore (d := d)) (fqOp P Q S b b') := by sorry

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