`BookProof.BookBrstYangMills.pderiv_X_mul` (i j : Fin 4 × Fin N) (p : FieldPoly N) : (pderiv i : Derivation ℂ (FieldPoly N) (FieldPoly N)) (X j * p) = (if i = j then p else 0) + X

Proved

BookProof.BookBrstYangMills.pderiv_X_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBookBrstYangMills.

BookProof.BookBrstYangMills.pderiv_X_mul (i j : Fin 4 × Fin N) (p : FieldPoly N) : (pderiv i : Derivation ℂ (FieldPoly N) (FieldPoly N)) (X j * p) = (if i = j then p else 0) + X j * pderiv i p

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

Preamble

-- Generated from ChapterBookBrstYangMills.lean — theorem BookProof.BookBrstYangMills.pderiv_X_mul
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.pderiv_X_mul (i j : Fin 4 × Fin N) (p : FieldPoly N) :
    (pderiv i : Derivation ℂ (FieldPoly N) (FieldPoly N)) (X j * p)
      = (if i = j then p else 0) + X j * pderiv i p := by sorry

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