`BookProof.NavierStokesGaugeY.uFieldOp_apply_of_y_zero` (u : Fin 3 → E →ₗ[ℂ] E) (uD : Fin 3 → Fin 3 → E →ₗ[ℂ] E) (Y : Fin 3 → E →ₗ[ℂ] E) (v : E) (hv : ∀ j, Y j v = 0)...

Proved

BookProof.NavierStokesGaugeY.uFieldOp_apply_of_y_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesGaugeY.

BookProof.NavierStokesGaugeY.uFieldOp_apply_of_y_zero (u : Fin 3 → E →ₗ[ℂ] E) (uD : Fin 3 → Fin 3 → E →ₗ[ℂ] E) (Y : Fin 3 → E →ₗ[ℂ] E) (v : E) (hv : ∀ j, Y j v = 0) (i : Fin 3) : uFieldOp u uD Y i v = u i v

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

Preamble

-- Generated from ChapterNavierStokesGaugeY.lean — theorem BookProof.NavierStokesGaugeY.uFieldOp_apply_of_y_zero
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.uFieldOp_apply_of_y_zero (u : Fin 3 → E →ₗ[ℂ] E) (uD : Fin 3 → Fin 3 → E →ₗ[ℂ] E)
    (Y : Fin 3 → E →ₗ[ℂ] E) (v : E) (hv : ∀ j, Y j v = 0) (i : Fin 3) :
    uFieldOp u uD Y i v = u i v := by sorry

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