`BookProof.ChapterG.no_shift_invariant_unit_vector` : ¬ ∃ Ψ : lp (fun _ : ℤ => ℂ) 2, ‖Ψ‖ = 1 ∧ ∀ k, Ψ (k + 1) = Ψ k

Proved

BookProof.ChapterG.no_shift_invariant_unit_vector

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG.

BookProof.ChapterG.no_shift_invariant_unit_vector : ¬ ∃ Ψ : lp (fun _ : ℤ => ℂ) 2, ‖Ψ‖ = 1 ∧ ∀ k, Ψ (k + 1) = Ψ k

Formalization note: Lean 4 identifier BookProof.ChapterG.no_shift_invariant_unit_vector.

Preamble

-- Generated from ChapterG.lean — theorem BookProof.ChapterG.no_shift_invariant_unit_vector
import Mathlib
import Definitions.Def_ChapterG
open BookProof.ChapterG


open scoped ComplexConjugate InnerProductSpace Matrix

Formal statement

theorem BookProof.ChapterG.no_shift_invariant_unit_vector :
    ¬ ∃ Ψ : lp (fun _ : ℤ => ℂ) 2, ‖Ψ‖ = 1 ∧ ∀ k, Ψ (k + 1) = Ψ k := by sorry

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