`BookProof.ChapterA3.mgammaZ_transpose` (μ : Fin 4) : (mgammaZ μ)ᵀ = (if μ = 0 then (-1 : ℤ) else 1) • mgammaZ μ

Proved

BookProof.ChapterA3.mgammaZ_transpose

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliCommutant.

BookProof.ChapterA3.mgammaZ_transpose (μ : Fin 4) : (mgammaZ μ)ᵀ = (if μ = 0 then (-1 : ℤ) else 1) • mgammaZ μ

Formalization note: Lean 4 identifier BookProof.ChapterA3.mgammaZ_transpose.

Preamble

-- Generated from ChapterPauliCommutant.lean — theorem BookProof.ChapterA3.mgammaZ_transpose
import Mathlib
import Definitions.Def_ChapterPauliCommutant
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix

Formal statement

theorem BookProof.ChapterA3.mgammaZ_transpose (μ : Fin 4) :
    (mgammaZ μ)ᵀ = (if μ = 0 then (-1 : ℤ) else 1) • mgammaZ μ := by sorry

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