`BookProof.NavierStokesGaugeY.pderiv_y_mul_uD` (m i j : Fin 3) (q : NSAlg) : pderiv (NSVar.y m) (X (NSVar.uD i j) * q) = X (NSVar.uD i j) * pderiv (NSVar.y m) q

Proved

BookProof.NavierStokesGaugeY.pderiv_y_mul_uD

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY.

BookProof.NavierStokesGaugeY.pderiv_y_mul_uD (m i j : Fin 3) (q : NSAlg) : pderiv (NSVar.y m) (X (NSVar.uD i j) * q) = X (NSVar.uD i j) * pderiv (NSVar.y m) q

Formalization note: Lean 4 identifier BookProof.NavierStokesGaugeY.pderiv_y_mul_uD.

Preamble

-- Generated from ChapterNavierStokesGaugeY.lean — theorem BookProof.NavierStokesGaugeY.pderiv_y_mul_uD
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Mathlib
import Definitions.Def_ChapterNavierStokesGaugeY
open BookProof.NavierStokesGaugeY



open MvPolynomial BookProof.NavierStokesFlow

Formal statement

theorem BookProof.NavierStokesGaugeY.pderiv_y_mul_uD (m i j : Fin 3) (q : NSAlg) :
    pderiv (NSVar.y m) (X (NSVar.uD i j) * q) = X (NSVar.uD i j) * pderiv (NSVar.y m) q := by sorry

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