`BookProof.BookBrstYangMills.gauss_const_identity` (μ : Fin 4) (a c e : Fin N) : (∑ b, G.f a b e * (-(G.D μ c b))) - (∑ b, G.f a b c * (-(G.D μ e b))) = ∑ h, G.f c e h * (-(G.D μ h

Proved

BookProof.BookBrstYangMills.gauss_const_identity

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.gauss_const_identity (μ : Fin 4) (a c e : Fin N) : (∑ b, G.f a b e * (-(G.D μ c b))) - (∑ b, G.f a b c * (-(G.D μ e b))) = ∑ h, G.f c e h * (-(G.D μ h a))

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

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.gauss_const_identity
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.gauss_const_identity (μ : Fin 4) (a c e : Fin N) :
    (∑ b, G.f a b e * (-(G.D μ c b))) - (∑ b, G.f a b c * (-(G.D μ e b)))
      = ∑ h, G.f c e h * (-(G.D μ h a)) := by sorry

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