`BookProof.ChapterA3.mgammaZ_clifford` (μ ν : Fin 4) : mgammaZ μ * mgammaZ ν + mgammaZ ν * mgammaZ μ = (-2 * minkowskiZ μ ν) • (1 : Matrix (Fin 4) (Fin 4) ℤ)

Proved

BookProof.ChapterA3.mgammaZ_clifford

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3.

BookProof.ChapterA3.mgammaZ_clifford (μ ν : Fin 4) : mgammaZ μ * mgammaZ ν + mgammaZ ν * mgammaZ μ = (-2 * minkowskiZ μ ν) • (1 : Matrix (Fin 4) (Fin 4) ℤ)

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

Preamble

-- Generated from ChapterA3.lean — theorem BookProof.ChapterA3.mgammaZ_clifford
import Mathlib
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix

Formal statement

theorem BookProof.ChapterA3.mgammaZ_clifford (μ ν : Fin 4) :
    mgammaZ μ * mgammaZ ν + mgammaZ ν * mgammaZ μ =
      (-2 * minkowskiZ μ ν) • (1 : Matrix (Fin 4) (Fin 4) ℤ) := by sorry

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