`BookProof.SmHamiltonian.smHamiltonian_quadForm_nonneg` (P : SmParams) (x : polyGaussCore (d := 163)) : 0 ≤ quadForm (smHamiltonian P) x

Proved

BookProof.SmHamiltonian.smHamiltonian_quadForm_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmHamiltonian.

BookProof.SmHamiltonian.smHamiltonian_quadForm_nonneg (P : SmParams) (x : polyGaussCore (d := 163)) : 0 ≤ quadForm (smHamiltonian P) x

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

Preamble

-- Generated from ChapterSmHamiltonian.lean — theorem BookProof.SmHamiltonian.smHamiltonian_quadForm_nonneg
import Definitions.Def_ChapterSmOneParticle
import Definitions.Def_ChapterYangMillsHermite
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_ChapterYangMillsFriedrichs
open BookProof.HermiteProductCore
open BookProof.YangMillsFriedrichs
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.smHamiltonian_quadForm_nonneg (P : SmParams) (x : polyGaussCore (d := 163)) :
    0 ≤ quadForm (smHamiltonian P) x := by sorry

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