`BookProof.QuantumGravityBrstCharge.affF_jacobi` (a b c h : Fin 19) : ∑ e, (affF a b e * affF e c h + affF b c e * affF e a h + affF c a e * affF e b h) = 0

Proved

BookProof.QuantumGravityBrstCharge.affF_jacobi

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantumGravityBrstCharge.

BookProof.QuantumGravityBrstCharge.affF_jacobi (a b c h : Fin 19) : ∑ e, (affF a b e * affF e c h + affF b c e * affF e a h + affF c a e * affF e b h) = 0

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

Preamble

-- Generated from ChapterQuantumGravityBrstCharge.lean — theorem BookProof.QuantumGravityBrstCharge.affF_jacobi
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterYangMillsHermite
import Definitions.Def_ChapterQuantumGravity3DGauge
import Mathlib
import Definitions.Def_ChapterQuantumGravityBrstCharge
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}
variable {d : ℕ}
variable {α : Type*}

Formal statement

theorem BookProof.QuantumGravityBrstCharge.affF_jacobi (a b c h : Fin 19) :
    ∑ e, (affF a b e * affF e c h + affF b c e * affF e a h + affF c a e * affF e b h) = 0 := by sorry

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