`BookProof.QuantumGravityBrstCharge.brst_abelian_nilpotent` (hCAR : GhostCAR χ β) (hcomm_chi : ∀ a b, G a * χ b = χ b * G a) (hcomm_beta : ∀ a b, G a * β b = β b * G a) (hab : ∀ a

Proved

BookProof.QuantumGravityBrstCharge.brst_abelian_nilpotent

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityBrstCharge.

BookProof.QuantumGravityBrstCharge.brst_abelian_nilpotent (hCAR : GhostCAR χ β) (hcomm_chi : ∀ a b, G a * χ b = χ b * G a) (hcomm_beta : ∀ a b, G a * β b = β b * G a) (hab : ∀ a b, G a * G b = G b * G a) : glin G χ * glin G χ = 0

Formalization note: Lean 4 identifier BookProof.QuantumGravityBrstCharge.brst_abelian_nilpotent.

Preamble

-- Generated from ChapterQuantumGravityBrstCharge.lean — theorem BookProof.QuantumGravityBrstCharge.brst_abelian_nilpotent
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterQuantumGravity3DGauge
import Mathlib
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Definitions.Def_ChapterBRSTNilpotent
open BookProof.BRSTNilpotent
open BookProof.QuantumGravityBrstCharge



open MvPolynomial BookProof.BRSTNilpotent BookProof.YangMillsHermite
open BookProof.QuantumGravity3DGauge

noncomputable section

variable {R : Type*} [Ring R] [Algebra ℝ R] {n : ℕ}
variable {f : Fin n → Fin n → Fin n → ℝ} {G χ β : Fin n → R}

Formal statement

theorem BookProof.QuantumGravityBrstCharge.brst_abelian_nilpotent (hCAR : GhostCAR χ β)
    (hcomm_chi : ∀ a b, G a * χ b = χ b * G a) (hcomm_beta : ∀ a b, G a * β b = β b * G a)
    (hab : ∀ a b, G a * G b = G b * G a) :
    glin G χ * glin G χ = 0 := by sorry

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