`BookProof.ChapterElectroweakFieldStrength.linear_trace` (G : Fin 3 → ℂ) (j : Fin 3) : ((∑ m, G m • ((1 / 2 : ℂ) • pauliV m)) * pauliV j).trace = G j

Proved

BookProof.ChapterElectroweakFieldStrength.linear_trace

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterElectroweakFieldStrength.

BookProof.ChapterElectroweakFieldStrength.linear_trace (G : Fin 3 → ℂ) (j : Fin 3) : ((∑ m, G m • ((1 / 2 : ℂ) • pauliV m)) * pauliV j).trace = G j

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

Preamble

-- Generated from ChapterElectroweakFieldStrength.lean — theorem BookProof.ChapterElectroweakFieldStrength.linear_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.linear_trace (G : Fin 3 → ℂ) (j : Fin 3) :
    ((∑ m, G m • ((1 / 2 : ℂ) • pauliV m)) * pauliV j).trace = G j := by sorry

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