`BookProof.ChapterGaugeShiftExample.shiftOp_adjoint` (m : ℤ) : ContinuousLinearMap.adjoint (shiftOp m) = shiftOp (-m)

Proved

BookProof.ChapterGaugeShiftExample.shiftOp_adjoint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeShiftExample.

BookProof.ChapterGaugeShiftExample.shiftOp_adjoint (m : ℤ) : ContinuousLinearMap.adjoint (shiftOp m) = shiftOp (-m)

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

Preamble

-- Generated from ChapterGaugeShiftExample.lean — theorem BookProof.ChapterGaugeShiftExample.shiftOp_adjoint
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_adjoint (m : ℤ) :
    ContinuousLinearMap.adjoint (shiftOp m) = shiftOp (-m) := by sorry

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