`BookProof.ChapterA3.sigmaZ_mul_transpose` : SigmaZ * SigmaZᵀ = (2 : ℤ) • (1 : Matrix (Fin 4) (Fin 4) ℤ)

Proved

BookProof.ChapterA3.sigmaZ_mul_transpose

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3i.

BookProof.ChapterA3.sigmaZ_mul_transpose : SigmaZ * SigmaZᵀ = (2 : ℤ) • (1 : Matrix (Fin 4) (Fin 4) ℤ)

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

Preamble

-- Generated from ChapterA3i.lean — theorem BookProof.ChapterA3.sigmaZ_mul_transpose
import Mathlib
import Definitions.Def_ChapterA3i
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.sigmaZ_mul_transpose :
    SigmaZ * SigmaZᵀ = (2 : ℤ) • (1 : Matrix (Fin 4) (Fin 4) ℤ) := by sorry

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