`BookProof.NavierStokesGaugeY.y_zero_of_commute` (Y : Fin 3 → E →ₗ[ℂ] E) (T : E →ₗ[ℂ] E) (hT : ∀ j, Y j ∘ₗ T = T ∘ₗ Y j) (v : E) (hv : ∀ j, Y j v = 0) (j : Fin 3) : Y j...

Proved

BookProof.NavierStokesGaugeY.y_zero_of_commute

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY.

BookProof.NavierStokesGaugeY.y_zero_of_commute (Y : Fin 3 → E →ₗ[ℂ] E) (T : E →ₗ[ℂ] E) (hT : ∀ j, Y j ∘ₗ T = T ∘ₗ Y j) (v : E) (hv : ∀ j, Y j v = 0) (j : Fin 3) : Y j (T v) = 0

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

Preamble

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



open MvPolynomial BookProof.NavierStokesFlow

variable {E : Type*} [AddCommGroup E] [Module ℂ E]

Formal statement

theorem BookProof.NavierStokesGaugeY.y_zero_of_commute (Y : Fin 3 → E →ₗ[ℂ] E) (T : E →ₗ[ℂ] E)
    (hT : ∀ j, Y j ∘ₗ T = T ∘ₗ Y j) (v : E) (hv : ∀ j, Y j v = 0) (j : Fin 3) :
    Y j (T v) = 0 := by sorry

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