`BookProof.NsBrstDerivativeGauge.glin_bos_apply_tmul` (G : Fin 3 → Module.End ℂ NSAlg) (p : NSAlg) (w : nsGhostSpace) : glin (fun j => nsBos (G j)) nsChi (p ⊗ₜ[ℂ] w) = ∑ j : Fin 3,

Proved

BookProof.NsBrstDerivativeGauge.glin_bos_apply_tmul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.glin_bos_apply_tmul (G : Fin 3 → Module.End ℂ NSAlg) (p : NSAlg) (w : nsGhostSpace) : glin (fun j => nsBos (G j)) nsChi (p ⊗ₜ[ℂ] w) = ∑ j : Fin 3, G j p ⊗ₜ[ℂ] nsGhostCre j w

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

Preamble

-- Generated from ChapterNsBrstDerivativeGauge.lean — theorem BookProof.NsBrstDerivativeGauge.glin_bos_apply_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.glin_bos_apply_tmul (G : Fin 3 → Module.End ℂ NSAlg) (p : NSAlg) (w : nsGhostSpace) :
    glin (fun j => nsBos (G j)) nsChi (p ⊗ₜ[ℂ] w)
      = ∑ j : Fin 3, G j p ⊗ₜ[ℂ] nsGhostCre j w := by sorry

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