`BookProof.SmHamiltonian.smPi_symmetricOn` (m : Fin 40) : SymmetricOn (polyGaussCore (d := 163)) ((polyGaussCore (d := 163)).subtype.comp (smPi m))

Proved

BookProof.SmHamiltonian.smPi_symmetricOn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmHamiltonian.

BookProof.SmHamiltonian.smPi_symmetricOn (m : Fin 40) : SymmetricOn (polyGaussCore (d := 163)) ((polyGaussCore (d := 163)).subtype.comp (smPi m))

Formalization note: Lean 4 identifier BookProof.SmHamiltonian.smPi_symmetricOn.

Preamble

-- Generated from ChapterSmHamiltonian.lean — theorem BookProof.SmHamiltonian.smPi_symmetricOn
import Definitions.Def_ChapterSmOneParticle
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFriedrichsExtension
import Mathlib
import Definitions.Def_ChapterSmHamiltonian
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterYangMillsHermite
open BookProof.HermiteProductCore
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.YangMillsHermite
open BookProof.SmHamiltonian



open MvPolynomial
open BookProof.SmOneParticle
open BookProof.YangMillsHermite BookProof.YangMillsFriedrichs
open BookProof.HermiteProductCore BookProof.FarisLavine
open BookProof.FriedrichsExtension

noncomputable section

variable {D : ℕ}

Formal statement

theorem BookProof.SmHamiltonian.smPi_symmetricOn (m : Fin 40) :
    SymmetricOn (polyGaussCore (d := 163))
      ((polyGaussCore (d := 163)).subtype.comp (smPi m)) := by sorry

View graph