`BookProof.ChapterElectroweakFieldStrength.electroweak_fieldStrength` (g : ℂ) (hg : g ≠ 0) (G Wμ Wν : Fin 3 → ℂ) (j : Fin 3) : proj g (Fmat g G Wμ Wν) j = G j - g * ∑ k, ∑ l, eps j

Proved

BookProof.ChapterElectroweakFieldStrength.electroweak_fieldStrength

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterElectroweakFieldStrength.

BookProof.ChapterElectroweakFieldStrength.electroweak_fieldStrength (g : ℂ) (hg : g ≠ 0) (G Wμ Wν : Fin 3 → ℂ) (j : Fin 3) : proj g (Fmat g G Wμ Wν) j = G j - g * ∑ k, ∑ l, eps j k l * Wμ k * Wν l

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

Preamble

-- Generated from ChapterElectroweakFieldStrength.lean — theorem BookProof.ChapterElectroweakFieldStrength.electroweak_fieldStrength
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.electroweak_fieldStrength (g : ℂ) (hg : g ≠ 0) (G Wμ Wν : Fin 3 → ℂ) (j : Fin 3) :
    proj g (Fmat g G Wμ Wν) j = G j - g * ∑ k, ∑ l, eps j k l * Wμ k * Wν l := by sorry

View graph