`BookProof.ChapterGammaCommutant.gamma_commutant_scalar` (X : Matrix (Fin 4) (Fin 4) ℂ) (h : ∀ μ, X * mgamma μ = mgamma μ * X) : X = X 0 0 • (1 : Matrix (Fin 4) (Fin 4) ℂ)

Proved

BookProof.ChapterGammaCommutant.gamma_commutant_scalar

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGammaCommutant.

BookProof.ChapterGammaCommutant.gamma_commutant_scalar (X : Matrix (Fin 4) (Fin 4) ℂ) (h : ∀ μ, X * mgamma μ = mgamma μ * X) : X = X 0 0 • (1 : Matrix (Fin 4) (Fin 4) ℂ)

Formalization note: Lean 4 identifier BookProof.ChapterGammaCommutant.gamma_commutant_scalar.

Preamble

-- Generated from ChapterGammaCommutant.lean — theorem BookProof.ChapterGammaCommutant.gamma_commutant_scalar
import Mathlib
import Definitions.Def_ChapterGammaCommutant
import Definitions.Def_ChapterA3
open BookProof.ChapterA3
open BookProof.ChapterGammaCommutant


open Matrix


open BookProof.ChapterA3

Formal statement

theorem BookProof.ChapterGammaCommutant.gamma_commutant_scalar (X : Matrix (Fin 4) (Fin 4) ℂ)
    (h : ∀ μ, X * mgamma μ = mgamma μ * X) :
    X = X 0 0 • (1 : Matrix (Fin 4) (Fin 4) ℂ) := by sorry

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