`BookProof.BookBrstYangMills.bosOpN_sum3` (T : Fin 4 → Fin N → Fin N → Module.End ℂ (FieldPoly N)) : bosOpN (∑ μ, ∑ a, ∑ b, T μ a b) = ∑ μ, ∑ a, ∑ b, bosOpN (T μ a b)

Proved

BookProof.BookBrstYangMills.bosOpN_sum3

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.bosOpN_sum3 (T : Fin 4 → Fin N → Fin N → Module.End ℂ (FieldPoly N)) : bosOpN (∑ μ, ∑ a, ∑ b, T μ a b) = ∑ μ, ∑ a, ∑ b, bosOpN (T μ a b)

Formalization note: Lean 4 identifier BookProof.BookBrstYangMills.bosOpN_sum3.

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.bosOpN_sum3
import Definitions.Def_ChapterBRSTNilpotent
import Definitions.Def_ChapterQuantumGravityBrstCharge
import Mathlib
import Definitions.Def_ChapterBookBrstYangMills
import Definitions.Def_ChapterYangMillsGhostSector
open BookProof.YangMillsGhost
open BookProof.BookBrstYangMills



open MvPolynomial BookProof.BRSTNilpotent BookProof.QuantumGravityBrstCharge

noncomputable section

variable {N : ℕ} (G : GaugeAlgebra N)

Formal statement

theorem BookProof.BookBrstYangMills.bosOpN_sum3 (T : Fin 4 → Fin N → Fin N → Module.End ℂ (FieldPoly N)) :
    bosOpN (∑ μ, ∑ a, ∑ b, T μ a b) = ∑ μ, ∑ a, ∑ b, bosOpN (T μ a b) := by sorry

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