`BookProof.SmBrstGhost.ghostNumber_comm_ghostCre` (m : ℕ) (a : Fin 12) : ghostNumber m * ghostCre m a - ghostCre m a * ghostNumber m = ghostCre m a

Proved

BookProof.SmBrstGhost.ghostNumber_comm_ghostCre

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSmBrstGhost.

BookProof.SmBrstGhost.ghostNumber_comm_ghostCre (m : ℕ) (a : Fin 12) : ghostNumber m * ghostCre m a - ghostCre m a * ghostNumber m = ghostCre m a

Formalization note: Lean 4 identifier BookProof.SmBrstGhost.ghostNumber_comm_ghostCre.

Preamble

-- Generated from ChapterSmBrstGhost.lean — theorem BookProof.SmBrstGhost.ghostNumber_comm_ghostCre
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsSU3
import Mathlib
import Definitions.Def_ChapterSmBrstGhost
import Definitions.Def_ChapterNavierStokes
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterSmCarAlgebra
open BookProof.NavierStokes
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.SmCar
open BookProof.SmBrstGhost



open BookProof.SmCar BookProof.BRSTNilpotent BookProof.YangMillsSU3

noncomputable section

variable {m : ℕ}

Formal statement

theorem BookProof.SmBrstGhost.ghostNumber_comm_ghostCre (m : ℕ) (a : Fin 12) :
    ghostNumber m * ghostCre m a - ghostCre m a * ghostNumber m = ghostCre m a := by sorry

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