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`BookProof.BookBrstYangMills.AfieldPoly_apply` (μ : Fin 4) (a : Fin N) (p : FieldPoly N) : AfieldPoly μ a p = X (μ, a) * p

Proved
BookProof.BookBrstYangMills.AfieldPoly_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.AfieldPoly_apply (μ : Fin 4) (a : Fin N) (p : FieldPoly N) : AfieldPoly μ a p = X (μ, a) * p

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

Preamble
-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.AfieldPoly_apply
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.AfieldPoly_apply (μ : Fin 4) (a : Fin N) (p : FieldPoly N) :
    AfieldPoly μ a p = X (μ, a) * p := by sorry

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