`BookProof.EnergyBandDecomposition.band_pairwise_disjoint` (hε : 0 < ε) (E : X → ℝ) : Pairwise (Function.onFun Disjoint (band E ε))

Proved

BookProof.EnergyBandDecomposition.band_pairwise_disjoint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEnergyBandDecomposition.

BookProof.EnergyBandDecomposition.band_pairwise_disjoint (hε : 0 < ε) (E : X → ℝ) : Pairwise (Function.onFun Disjoint (band E ε))

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

Preamble

-- Generated from ChapterEnergyBandDecomposition.lean — theorem BookProof.EnergyBandDecomposition.band_pairwise_disjoint
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.band_pairwise_disjoint (hε : 0 < ε) (E : X → ℝ) :
    Pairwise (Function.onFun Disjoint (band E ε)) := by sorry

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