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`BookProof.ChapterGaugeShiftExample.velocityOp_commute` (v w : LinfZ) : velocityOp v * velocityOp w = velocityOp w * velocityOp v

Proved
BookProof.ChapterGaugeShiftExample.velocityOp_commute

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeShiftExample.

BookProof.ChapterGaugeShiftExample.velocityOp_commute (v w : LinfZ) : velocityOp v * velocityOp w = velocityOp w * velocityOp v

Formalization note: Lean 4 identifier BookProof.ChapterGaugeShiftExample.velocityOp_commute.

Preamble
-- Generated from ChapterGaugeShiftExample.lean — theorem BookProof.ChapterGaugeShiftExample.velocityOp_commute
import Mathlib
import Definitions.Def_ChapterGaugeShiftExample
import Definitions.Def_ChapterContinuityUnitary
import Definitions.Def_ChapterContinuityUnitaryInfinite
open BookProof.ChapterContinuityUnitary
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.ChapterGaugeShiftExample


open scoped InnerProductSpace


open BookProof.ChapterContinuityUnitaryInfinite
Formal statement
theorem BookProof.ChapterGaugeShiftExample.velocityOp_commute (v w : LinfZ) :
    velocityOp v * velocityOp w = velocityOp w * velocityOp v := by sorry

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