`BookProof.BookBrstYangMills.Afield_comm_chi` (μ : Fin 4) (a b : Fin N) : Afield (N := N) μ a * chiOp b = chiOp b * Afield μ a

Proved

BookProof.BookBrstYangMills.Afield_comm_chi

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.Afield_comm_chi (μ : Fin 4) (a b : Fin N) : Afield (N := N) μ a * chiOp b = chiOp b * Afield μ a

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

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.Afield_comm_chi
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
import Definitions.Def_ChapterYangMillsGhostSector
open BookProof.YangMillsGhost
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)

Formal statement

theorem BookProof.BookBrstYangMills.Afield_comm_chi (μ : Fin 4) (a b : Fin N) :
    Afield (N := N) μ a * chiOp b = chiOp b * Afield μ a := by sorry

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