`BookProof.NavierStokesGaugeY.genY_shifts_velocity` (i j : Fin 3) (p : NSAlg) : genY j (X (NSVar.u i) * p) - X (NSVar.u i) * genY j p = -(X (NSVar.uD i j) * p)

Proved

BookProof.NavierStokesGaugeY.genY_shifts_velocity

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY.

BookProof.NavierStokesGaugeY.genY_shifts_velocity (i j : Fin 3) (p : NSAlg) : genY j (X (NSVar.u i) * p) - X (NSVar.u i) * genY j p = -(X (NSVar.uD i j) * p)

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

Preamble

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



open MvPolynomial BookProof.NavierStokesFlow

Formal statement

theorem BookProof.NavierStokesGaugeY.genY_shifts_velocity (i j : Fin 3) (p : NSAlg) :
    genY j (X (NSVar.u i) * p) - X (NSVar.u i) * genY j p = -(X (NSVar.uD i j) * p) := by sorry

View graph