Prove2Me

`BookProof.ChapterElectroweakFieldStrength.pauli_commutator_trace` (k l j : Fin 3) : ((pauliV k * pauliV l - pauliV l * pauliV k) * pauliV j).trace = 4 * Complex.I * eps k l j

Proved
BookProof.ChapterElectroweakFieldStrength.pauli_commutator_trace

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterElectroweakFieldStrength.

BookProof.ChapterElectroweakFieldStrength.pauli_commutator_trace (k l j : Fin 3) : ((pauliV k * pauliV l - pauliV l * pauliV k) * pauliV j).trace = 4 * Complex.I * eps k l j

Formalization note: Lean 4 identifier BookProof.ChapterElectroweakFieldStrength.pauli_commutator_trace.

Preamble
-- Generated from ChapterElectroweakFieldStrength.lean — theorem BookProof.ChapterElectroweakFieldStrength.pauli_commutator_trace
import Definitions.Def_ChapterParity
import Mathlib
import Definitions.Def_ChapterElectroweakFieldStrength
import Definitions.Def_ChapterParitySU2
open BookProof.ChapterParitySU2
open BookProof.ChapterElectroweakFieldStrength


open Matrix


open BookProof.ChapterParity BookProof.ChapterParitySU2
Formal statement
theorem BookProof.ChapterElectroweakFieldStrength.pauli_commutator_trace (k l j : Fin 3) :
    ((pauliV k * pauliV l - pauliV l * pauliV k) * pauliV j).trace = 4 * Complex.I * eps k l j := by sorry

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