Prove2Me

`BookProof.NsBrstDerivativeGauge.genU_leibniz` (i : Fin 3) (p q : NSAlg) : genU i (p * q) = genU i p * q + p * genU i q

Proved
BookProof.NsBrstDerivativeGauge.genU_leibniz

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.genU_leibniz (i : Fin 3) (p q : NSAlg) : genU i (p * q) = genU i p * q + p * genU i q

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

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



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

noncomputable section
Formal statement
theorem BookProof.NsBrstDerivativeGauge.genU_leibniz (i : Fin 3) (p q : NSAlg) :
    genU i (p * q) = genU i p * q + p * genU i q := by sorry

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