`BookProof.NsBrstDerivativeGauge.ghostComponent_tmul` (p : NSAlg) (w : nsGhostSpace) : ghostComponent (p ⊗ₜ[ℂ] w) = (MvPolynomial.aeval (fun _ => (0 : ℂ)) p) • w

Proved

BookProof.NsBrstDerivativeGauge.ghostComponent_tmul

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.ghostComponent_tmul (p : NSAlg) (w : nsGhostSpace) : ghostComponent (p ⊗ₜ[ℂ] w) = (MvPolynomial.aeval (fun _ => (0 : ℂ)) p) • w

Formalization note: Lean 4 identifier BookProof.NsBrstDerivativeGauge.ghostComponent_tmul.

Preamble

-- Generated from ChapterNsBrstDerivativeGauge.lean — theorem BookProof.NsBrstDerivativeGauge.ghostComponent_tmul
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Definitions.Def_ChapterNavierStokesGaugeY2
import Mathlib
import Definitions.Def_ChapterNsBrstDerivativeGauge
import Definitions.Def_ChapterNavierStokesGaugeY
open BookProof.NavierStokesGaugeY
open BookProof.NsBrstDerivativeGauge



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge
open BookProof.NavierStokesGaugeY BookProof.NavierStokesGaugeY2

noncomputable section

Formal statement

theorem BookProof.NsBrstDerivativeGauge.ghostComponent_tmul (p : NSAlg) (w : nsGhostSpace) :
    ghostComponent (p ⊗ₜ[ℂ] w) = (MvPolynomial.aeval (fun _ => (0 : ℂ)) p) • w := by sorry

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