`BookProof.NsBrstDerivativeGauge.genY2_comm_genU` (i j : Fin 3) : genY2 j * genU i = genU i * genY2 j

Proved

BookProof.NsBrstDerivativeGauge.genY2_comm_genU

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.genY2_comm_genU (i j : Fin 3) : genY2 j * genU i = genU i * genY2 j

Formalization note: Lean 4 identifier BookProof.NsBrstDerivativeGauge.genY2_comm_genU.

Preamble

-- Generated from ChapterNsBrstDerivativeGauge.lean — theorem BookProof.NsBrstDerivativeGauge.genY2_comm_genU
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterNsBrstDerivativeGauge
import Definitions.Def_ChapterNavierStokesGaugeY
import Definitions.Def_ChapterNavierStokesGaugeY2
open BookProof.NavierStokesGaugeY
open BookProof.NavierStokesGaugeY2
open BookProof.NsBrstDerivativeGauge



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge
open BookProof.NavierStokesGaugeY BookProof.NavierStokesGaugeY2

noncomputable section

Formal statement

theorem BookProof.NsBrstDerivativeGauge.genY2_comm_genU (i j : Fin 3) : genY2 j * genU i = genU i * genY2 j := by sorry

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