`BookProof.QuantizationWeyl.weyl` (a b : ℝ) : NormedSpace.exp (a • Xgen) * NormedSpace.exp (b • Ygen) = NormedSpace.exp (a • Xgen + b • Ygen + (a * b / 2) • Zgen)

Proved

BookProof.QuantizationWeyl.weyl

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterQuantizationWeyl.

BookProof.QuantizationWeyl.weyl (a b : ℝ) : NormedSpace.exp (a • Xgen) * NormedSpace.exp (b • Ygen) = NormedSpace.exp (a • Xgen + b • Ygen + (a * b / 2) • Zgen)

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

Preamble

-- Generated from ChapterQuantizationWeyl.lean — theorem BookProof.QuantizationWeyl.weyl
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.weyl (a b : ℝ) :
    NormedSpace.exp (a • Xgen) * NormedSpace.exp (b • Ygen)
      = NormedSpace.exp (a • Xgen + b • Ygen + (a * b / 2) • Zgen) := by sorry

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