`BookProof.LocalOperators.not_translationInvariant_of_pointSupported` (hd : 0 < d) (l : LocalField d E) (x₀ : Fin d → ℝ) (hne : l x₀ ≠ 0) (hsupp : ∀ z, z ≠ x₀ → l z = 0) : ¬ Transl

Proved

BookProof.LocalOperators.not_translationInvariant_of_pointSupported

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLocalOperators.

BookProof.LocalOperators.not_translationInvariant_of_pointSupported (hd : 0 < d) (l : LocalField d E) (x₀ : Fin d → ℝ) (hne : l x₀ ≠ 0) (hsupp : ∀ z, z ≠ x₀ → l z = 0) : ¬ TranslationInvariant l

Formalization note: Lean 4 identifier BookProof.LocalOperators.not_translationInvariant_of_pointSupported.

Preamble

-- Generated from ChapterLocalOperators.lean — theorem BookProof.LocalOperators.not_translationInvariant_of_pointSupported
import Mathlib
import Definitions.Def_ChapterLocalOperators
open BookProof.LocalOperators



open MeasureTheory

variable {d : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.LocalOperators.not_translationInvariant_of_pointSupported
    (hd : 0 < d) (l : LocalField d E) (x₀ : Fin d → ℝ)
    (hne : l x₀ ≠ 0) (hsupp : ∀ z, z ≠ x₀ → l z = 0) :
    ¬ TranslationInvariant l := by sorry

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