Prove2Me

`BookProof.BookBrstYangMills.bosOpN_ghostOpN_comm` (S : Module.End ℂ (FieldPoly N)) (T : Module.End ℂ (GhostSpace N)) : bosOpN S * ghostOpN T = ghostOpN T * bosOpN S

Proved
BookProof.BookBrstYangMills.bosOpN_ghostOpN_comm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.bosOpN_ghostOpN_comm (S : Module.End ℂ (FieldPoly N)) (T : Module.End ℂ (GhostSpace N)) : bosOpN S * ghostOpN T = ghostOpN T * bosOpN S

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

Preamble
-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.bosOpN_ghostOpN_comm
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.bosOpN_ghostOpN_comm (S : Module.End ℂ (FieldPoly N)) (T : Module.End ℂ (GhostSpace N)) :
    bosOpN S * ghostOpN T = ghostOpN T * bosOpN S := by sorry

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