Prove2Me

`BookProof.BookBrstYangMills.gaussDer_bracket` (c e : Fin N) : ⁅gaussDer G c, gaussDer G e⁆ = ∑ h, ((G.f c e h : ℝ) : ℂ) • gaussDer G h

Proved
BookProof.BookBrstYangMills.gaussDer_bracket

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.gaussDer_bracket (c e : Fin N) : ⁅gaussDer G c, gaussDer G e⁆ = ∑ h, ((G.f c e h : ℝ) : ℂ) • gaussDer G h

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

Preamble
-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.gaussDer_bracket
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_bracket (c e : Fin N) :
    ⁅gaussDer G c, gaussDer G e⁆
      = ∑ h, ((G.f c e h : ℝ) : ℂ) • gaussDer G h := by sorry

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