`BookProof.NavierStokesGaugeY.uField_pderiv_y` (i j : Fin 3) : pderiv (NSVar.y j) (uField i) = X (NSVar.uD i j)

Proved

BookProof.NavierStokesGaugeY.uField_pderiv_y

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY.

BookProof.NavierStokesGaugeY.uField_pderiv_y (i j : Fin 3) : pderiv (NSVar.y j) (uField i) = X (NSVar.uD i j)

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

Preamble

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



open MvPolynomial BookProof.NavierStokesFlow

Formal statement

theorem BookProof.NavierStokesGaugeY.uField_pderiv_y (i j : Fin 3) :
    pderiv (NSVar.y j) (uField i) = X (NSVar.uD i j) := by sorry

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