`BookProof.NavierStokesGaugeY2.uField2_pderiv_y_twice` (i j : Fin 3) : pderiv (NSVar.y j) (pderiv (NSVar.y j) (uField2 i)) = X (NSVar.uL i)

Proved

BookProof.NavierStokesGaugeY2.uField2_pderiv_y_twice

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY2.

BookProof.NavierStokesGaugeY2.uField2_pderiv_y_twice (i j : Fin 3) : pderiv (NSVar.y j) (pderiv (NSVar.y j) (uField2 i)) = X (NSVar.uL i)

Formalization note: Lean 4 identifier BookProof.NavierStokesGaugeY2.uField2_pderiv_y_twice.

Preamble

-- Generated from ChapterNavierStokesGaugeY2.lean — theorem BookProof.NavierStokesGaugeY2.uField2_pderiv_y_twice
import Mathlib
import Definitions.Def_ChapterNavierStokesGaugeY2
import Definitions.Def_ChapterNavierStokesGaugeY
open BookProof.NavierStokesGaugeY
open BookProof.NavierStokesGaugeY2



open MvPolynomial BookProof.NavierStokesGaugeY

Formal statement

theorem BookProof.NavierStokesGaugeY2.uField2_pderiv_y_twice (i j : Fin 3) :
    pderiv (NSVar.y j) (pderiv (NSVar.y j) (uField2 i)) = X (NSVar.uL i) := by sorry

View graph