`BookProof.ChapterGaugeShiftExample.shiftOp_eq_self_iff` {m : ℤ} (hm : m ≠ 0) {f : L2Z} (hf : shiftOp m f = f) : f = 0

Proved

BookProof.ChapterGaugeShiftExample.shiftOp_eq_self_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeShiftExample.

BookProof.ChapterGaugeShiftExample.shiftOp_eq_self_iff {m : ℤ} (hm : m ≠ 0) {f : L2Z} (hf : shiftOp m f = f) : f = 0

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

Preamble

-- Generated from ChapterGaugeShiftExample.lean — theorem BookProof.ChapterGaugeShiftExample.shiftOp_eq_self_iff
import Mathlib
import Definitions.Def_ChapterGaugeShiftExample
import Definitions.Def_ChapterContinuityUnitaryInfinite
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.ChapterGaugeShiftExample


open scoped InnerProductSpace


open BookProof.ChapterContinuityUnitaryInfinite

Formal statement

theorem BookProof.ChapterGaugeShiftExample.shiftOp_eq_self_iff {m : ℤ} (hm : m ≠ 0) {f : L2Z} (hf : shiftOp m f = f) :
    f = 0 := by sorry

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