`BookProof.ChapterGaugeShiftExample.velocityOp_basisVecL2` (v : LinfZ) (j : ℤ) : velocityOp v (basisVecL2 j) = ((v : ℤ → ℝ) j : ℂ) • basisVecL2 j

Proved

BookProof.ChapterGaugeShiftExample.velocityOp_basisVecL2

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeShiftExample.

BookProof.ChapterGaugeShiftExample.velocityOp_basisVecL2 (v : LinfZ) (j : ℤ) : velocityOp v (basisVecL2 j) = ((v : ℤ → ℝ) j : ℂ) • basisVecL2 j

Formalization note: Lean 4 identifier BookProof.ChapterGaugeShiftExample.velocityOp_basisVecL2.

Preamble

-- Generated from ChapterGaugeShiftExample.lean — theorem BookProof.ChapterGaugeShiftExample.velocityOp_basisVecL2
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_basisVecL2 (v : LinfZ) (j : ℤ) :
    velocityOp v (basisVecL2 j) = ((v : ℤ → ℝ) j : ℂ) • basisVecL2 j := by sorry

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