`BookProof.NavierStokesGaugeY2.genY2_uField` (i j : Fin 3) : genY2 j (uField i) = -(X (NSVar.uL i) * X (NSVar.y j))

Proved

BookProof.NavierStokesGaugeY2.genY2_uField

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY2.

BookProof.NavierStokesGaugeY2.genY2_uField (i j : Fin 3) : genY2 j (uField i) = -(X (NSVar.uL i) * X (NSVar.y j))

Formalization note: Lean 4 identifier BookProof.NavierStokesGaugeY2.genY2_uField.

Preamble

-- Generated from ChapterNavierStokesGaugeY2.lean — theorem BookProof.NavierStokesGaugeY2.genY2_uField
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.genY2_uField (i j : Fin 3) :
    genY2 j (uField i) = -(X (NSVar.uL i) * X (NSVar.y j)) := by sorry

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