`BookProof.NavierStokesGaugeY2.genY2_uField2_perturbed` (i j : Fin 3) (c : ℂ) : genY2 j (uField2 i + C c * (X (NSVar.y j) * X (NSVar.y j))) = C c * (2 * X (NSVar.y j))

Proved

BookProof.NavierStokesGaugeY2.genY2_uField2_perturbed

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY2.

BookProof.NavierStokesGaugeY2.genY2_uField2_perturbed (i j : Fin 3) (c : ℂ) : genY2 j (uField2 i + C c * (X (NSVar.y j) * X (NSVar.y j))) = C c * (2 * X (NSVar.y j))

Formalization note: Lean 4 identifier BookProof.NavierStokesGaugeY2.genY2_uField2_perturbed.

Preamble

-- Generated from ChapterNavierStokesGaugeY2.lean — theorem BookProof.NavierStokesGaugeY2.genY2_uField2_perturbed
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_uField2_perturbed (i j : Fin 3) (c : ℂ) :
    genY2 j (uField2 i + C c * (X (NSVar.y j) * X (NSVar.y j)))
      = C c * (2 * X (NSVar.y j)) := by sorry

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