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`BookProof.BookBrstYangMills.gaussGenPoly_bracket` (c e : Fin N) : gaussGenPoly G c * gaussGenPoly G e - gaussGenPoly G e * gaussGenPoly G c = ∑ h, (G.f c e h) • gaussGenPoly G h

Proved
BookProof.BookBrstYangMills.gaussGenPoly_bracket

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.gaussGenPoly_bracket (c e : Fin N) : gaussGenPoly G c * gaussGenPoly G e - gaussGenPoly G e * gaussGenPoly G c = ∑ h, (G.f c e h) • gaussGenPoly G h

Formalization note: Lean 4 identifier BookProof.BookBrstYangMills.gaussGenPoly_bracket.

Preamble
-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.gaussGenPoly_bracket
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)
Formal statement
theorem BookProof.BookBrstYangMills.gaussGenPoly_bracket (c e : Fin N) :
    gaussGenPoly G c * gaussGenPoly G e - gaussGenPoly G e * gaussGenPoly G c
      = ∑ h, (G.f c e h) • gaussGenPoly G h := by sorry

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