`BookProof.BookBrstYangMills.I_smul_gaussGen` (c : Fin N) : Complex.I • gaussGen G c = (∑ μ, ∑ a, ((G.D μ c a : ℝ) : ℂ) • mom μ a) - (∑ μ, ∑ a, ∑ b, ((G.f a b c : ℝ) :...

Proved

BookProof.BookBrstYangMills.I_smul_gaussGen

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.I_smul_gaussGen (c : Fin N) : Complex.I • gaussGen G c = (∑ μ, ∑ a, ((G.D μ c a : ℝ) : ℂ) • mom μ a) - (∑ μ, ∑ a, ∑ b, ((G.f a b c : ℝ) : ℂ) • (mom μ a * Afield μ b))

Formalization note: Lean 4 identifier BookProof.BookBrstYangMills.I_smul_gaussGen.

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.I_smul_gaussGen
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
import Definitions.Def_ChapterNavierStokesCanonicalVector
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterYangMillsGhostSector
open BookProof.NavierStokesFlow.CanonicalVector
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.YangMillsGhost
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)

Formal statement

theorem BookProof.BookBrstYangMills.I_smul_gaussGen (c : Fin N) :
    Complex.I • gaussGen G c
      = (∑ μ, ∑ a, ((G.D μ c a : ℝ) : ℂ) • mom μ a)
        - (∑ μ, ∑ a, ∑ b, ((G.f a b c : ℝ) : ℂ) • (mom μ a * Afield μ b)) := by sorry

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