`BookProof.NsBrstDerivativeGauge.nsBos_nsGh_apply_tmul` (S : Module.End ℂ NSAlg) (T : Module.End ℂ nsGhostSpace) (p : NSAlg) (w : nsGhostSpace) : (nsBos S * nsGh T) (p ⊗ₜ[ℂ] w) = S

Proved

BookProof.NsBrstDerivativeGauge.nsBos_nsGh_apply_tmul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsBrstDerivativeGauge.

BookProof.NsBrstDerivativeGauge.nsBos_nsGh_apply_tmul (S : Module.End ℂ NSAlg) (T : Module.End ℂ nsGhostSpace) (p : NSAlg) (w : nsGhostSpace) : (nsBos S * nsGh T) (p ⊗ₜ[ℂ] w) = S p ⊗ₜ[ℂ] T w

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

Preamble

-- Generated from ChapterNsBrstDerivativeGauge.lean — theorem BookProof.NsBrstDerivativeGauge.nsBos_nsGh_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.nsBos_nsGh_apply_tmul (S : Module.End ℂ NSAlg) (T : Module.End ℂ nsGhostSpace)
    (p : NSAlg) (w : nsGhostSpace) :
    (nsBos S * nsGh T) (p ⊗ₜ[ℂ] w) = S p ⊗ₜ[ℂ] T w := by sorry

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