`BookProof.QuantumGravityBrstCharge.chi_comm_pair` (hCAR : GhostCAR χ β) (a d g : Fin n) : χ a * (χ d * χ g) = (χ d * χ g) * χ a

Proved

BookProof.QuantumGravityBrstCharge.chi_comm_pair

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityBrstCharge.

BookProof.QuantumGravityBrstCharge.chi_comm_pair (hCAR : GhostCAR χ β) (a d g : Fin n) : χ a * (χ d * χ g) = (χ d * χ g) * χ a

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

Preamble

-- Generated from ChapterQuantumGravityBrstCharge.lean — theorem BookProof.QuantumGravityBrstCharge.chi_comm_pair
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.chi_comm_pair (hCAR : GhostCAR χ β) (a d g : Fin n) :
    χ a * (χ d * χ g) = (χ d * χ g) * χ a := by sorry

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