`BookProof.EnergyBandDecomposition.evolution_preserves_band` (t : ℝ) (f : X → ℂ) (k : ℤ) : Function.support (fun x => Complex.exp (-(Complex.I * (t * E x))) * bandPart E ε k f x) ⊆

Proved

BookProof.EnergyBandDecomposition.evolution_preserves_band

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEnergyBandDecomposition.

BookProof.EnergyBandDecomposition.evolution_preserves_band (t : ℝ) (f : X → ℂ) (k : ℤ) : Function.support (fun x => Complex.exp (-(Complex.I * (t * E x))) * bandPart E ε k f x) ⊆ band E ε k

Formalization note: Lean 4 identifier BookProof.EnergyBandDecomposition.evolution_preserves_band.

Preamble

-- Generated from ChapterEnergyBandDecomposition.lean — theorem BookProof.EnergyBandDecomposition.evolution_preserves_band
import Mathlib
import Definitions.Def_ChapterEnergyBandDecomposition
open BookProof.EnergyBandDecomposition



open MeasureTheory

variable {X : Type*} {E : X → ℝ} {ε : ℝ} {k : ℤ} {x : X}

Formal statement

theorem BookProof.EnergyBandDecomposition.evolution_preserves_band (t : ℝ) (f : X → ℂ) (k : ℤ) :
    Function.support (fun x => Complex.exp (-(Complex.I * (t * E x))) * bandPart E ε k f x)
      ⊆ band E ε k := by sorry

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