`BookProof.BookBrstYangMills.gaussDer_vecComb` (c : Fin N) (α : ℝ) (β : Fin N → ℝ) (μ : Fin 4) : gaussDer G c (vecComb α β μ) = vecComb (∑ b, β b * (-(G.D μ c b))) (fun g => ∑ b, β

Proved

BookProof.BookBrstYangMills.gaussDer_vecComb

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.gaussDer_vecComb (c : Fin N) (α : ℝ) (β : Fin N → ℝ) (μ : Fin 4) : gaussDer G c (vecComb α β μ) = vecComb (∑ b, β b * (-(G.D μ c b))) (fun g => ∑ b, β b * G.f b g c) μ

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

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.gaussDer_vecComb
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)

Formal statement

theorem BookProof.BookBrstYangMills.gaussDer_vecComb (c : Fin N) (α : ℝ) (β : Fin N → ℝ) (μ : Fin 4) :
    gaussDer G c (vecComb α β μ)
      = vecComb (∑ b, β b * (-(G.D μ c b))) (fun g => ∑ b, β b * G.f b g c) μ := by sorry

View graph