`BookProof.ChapterA3.paulisigma_trace` (μ ν : Fin 4) : (pauliσ μ * pauliσ ν).trace = if μ = ν then 2 else 0

Proved

BookProof.ChapterA3.paulisigma_trace

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.paulisigma_trace (μ ν : Fin 4) : (pauliσ μ * pauliσ ν).trace = if μ = ν then 2 else 0

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

Preamble

-- Generated from ChapterA3h.lean — theorem BookProof.ChapterA3.pauliσ_trace
import Mathlib
import Definitions.Def_ChapterA3h
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.paulisigma_trace (μ ν : Fin 4) :
    (pauliσ μ * pauliσ ν).trace = if μ = ν then 2 else 0 := by sorry

View graph