`BookProof.ChapterGaugeMechanicsCharge.mul_commutes_chargeQ_iff_euler_zero` (g : P) : (∀ p : P, chargeQ (g * p) = g * chargeQ p) ↔ eulerOp g = 0

Proved

BookProof.ChapterGaugeMechanicsCharge.mul_commutes_chargeQ_iff_euler_zero

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeMechanicsCharge.

BookProof.ChapterGaugeMechanicsCharge.mul_commutes_chargeQ_iff_euler_zero (g : P) : (∀ p : P, chargeQ (g * p) = g * chargeQ p) ↔ eulerOp g = 0

Formalization note: Lean 4 identifier BookProof.ChapterGaugeMechanicsCharge.mul_commutes_chargeQ_iff_euler_zero.

Preamble

-- Generated from ChapterGaugeMechanicsCharge.lean — theorem BookProof.ChapterGaugeMechanicsCharge.mul_commutes_chargeQ_iff_euler_zero
import Mathlib
import Definitions.Def_ChapterGaugeMechanicsCharge
open BookProof.ChapterGaugeMechanicsCharge




open MvPolynomial

Formal statement

theorem BookProof.ChapterGaugeMechanicsCharge.mul_commutes_chargeQ_iff_euler_zero (g : P) :
    (∀ p : P, chargeQ (g * p) = g * chargeQ p) ↔ eulerOp g = 0 := by sorry

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