`BookProof.NsBrstDerivativeGauge.pderiv_u_mul_uL` (m i : Fin 3) (q : NSAlg) : pderiv (NSVar.u m) (X (NSVar.uL i) * q) = X (NSVar.uL i) * pderiv (NSVar.u m) q

Proved

BookProof.NsBrstDerivativeGauge.pderiv_u_mul_uL

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.pderiv_u_mul_uL (m i : Fin 3) (q : NSAlg) : pderiv (NSVar.u m) (X (NSVar.uL i) * q) = X (NSVar.uL i) * pderiv (NSVar.u m) q

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

Preamble

-- Generated from ChapterNsBrstDerivativeGauge.lean — theorem BookProof.NsBrstDerivativeGauge.pderiv_u_mul_uL
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.pderiv_u_mul_uL (m i : Fin 3) (q : NSAlg) :
    pderiv (NSVar.u m) (X (NSVar.uL i) * q) = X (NSVar.uL i) * pderiv (NSVar.u m) q := by sorry

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