`BookProof.NavierStokesGaugeY.genX_ccr_x` (j k : Fin 3) (p : NSAlg) : genX j (X (NSVar.x k) * p) - X (NSVar.x k) * genX j p = if NSVar.x j = NSVar.x k then p else 0

Proved

BookProof.NavierStokesGaugeY.genX_ccr_x

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY.

BookProof.NavierStokesGaugeY.genX_ccr_x (j k : Fin 3) (p : NSAlg) : genX j (X (NSVar.x k) * p) - X (NSVar.x k) * genX j p = if NSVar.x j = NSVar.x k then p else 0

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

Preamble

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



open MvPolynomial BookProof.NavierStokesFlow

Formal statement

theorem BookProof.NavierStokesGaugeY.genX_ccr_x (j k : Fin 3) (p : NSAlg) :
    genX j (X (NSVar.x k) * p) - X (NSVar.x k) * genX j p
      = if NSVar.x j = NSVar.x k then p else 0 := by sorry

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