`BookProof.QuantizationWeyl.Zgen_central` : Xgen * Zgen = 0 ∧ Zgen * Xgen = 0 ∧ Ygen * Zgen = 0 ∧ Zgen * Ygen = 0

Proved

BookProof.QuantizationWeyl.Zgen_central

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantizationWeyl.

BookProof.QuantizationWeyl.Zgen_central : Xgen * Zgen = 0 ∧ Zgen * Xgen = 0 ∧ Ygen * Zgen = 0 ∧ Zgen * Ygen = 0

Formalization note: Lean 4 identifier BookProof.QuantizationWeyl.Zgen_central.

Preamble

-- Generated from ChapterQuantizationWeyl.lean — theorem BookProof.QuantizationWeyl.Zgen_central
import Mathlib
import Definitions.Def_ChapterQuantizationWeyl
open BookProof.QuantizationWeyl


open NormedSpace
open scoped Matrix


attribute [local instance] Matrix.linftyOpNormedRing Matrix.linftyOpNormedAlgebra

Formal statement

theorem BookProof.QuantizationWeyl.Zgen_central : Xgen * Zgen = 0 ∧ Zgen * Xgen = 0 ∧ Ygen * Zgen = 0 ∧ Zgen * Ygen = 0 := by sorry

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