`BookProof.ChapterPauliFundamental.G_transpose_mul` (μ : Fin 4) (T : Finset (Fin 4)) : (G T)ᵀ * mgamma μ = sgnT μ (stepT μ T) • (G (stepT μ T))ᵀ

Proved

BookProof.ChapterPauliFundamental.G_transpose_mul

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliFundamental.

BookProof.ChapterPauliFundamental.G_transpose_mul (μ : Fin 4) (T : Finset (Fin 4)) : (G T)ᵀ * mgamma μ = sgnT μ (stepT μ T) • (G (stepT μ T))ᵀ

Formalization note: Lean 4 identifier BookProof.ChapterPauliFundamental.G_transpose_mul.

Preamble

-- Generated from ChapterPauliFundamental.lean — theorem BookProof.ChapterPauliFundamental.G_transpose_mul
import Definitions.Def_ChapterGammaCommutant
import Mathlib
import Definitions.Def_ChapterPauliFundamental
import Definitions.Def_ChapterA3
open BookProof.ChapterA3
open BookProof.ChapterPauliFundamental


open Matrix Finset


open BookProof.ChapterA3 BookProof.ChapterGammaCommutant

variable {A : Fin 4 → M4}

Formal statement

theorem BookProof.ChapterPauliFundamental.G_transpose_mul (μ : Fin 4) (T : Finset (Fin 4)) :
    (G T)ᵀ * mgamma μ = sgnT μ (stepT μ T) • (G (stepT μ T))ᵀ := by sorry

View graph