Prove2Me

`BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol_sub_self_le` {Emax : ℝ} (h : EnergyLimited E μ Emax f) (t : ℝ) : eLpNorm (evol E t f - f) 2 μ ≤ ENNReal.ofReal (|t| * Emax) *

Proved
BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol_sub_self_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEnergyBoundedEvolution.

BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol_sub_self_le {Emax : ℝ} (h : EnergyLimited E μ Emax f) (t : ℝ) : eLpNorm (evol E t f - f) 2 μ ≤ ENNReal.ofReal (|t| * Emax) * eLpNorm f 2 μ

Formalization note: Lean 4 identifier BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol_sub_self_le.

Preamble
-- Generated from ChapterEnergyBoundedEvolution.lean — theorem BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol_sub_self_le
import Definitions.Def_ChapterEnergyBandDecomposition
import Mathlib
import Definitions.Def_ChapterEnergyBoundedEvolution
open BookProof.ChapterEnergyBoundedEvolution



open MeasureTheory Complex
open scoped ENNReal
open BookProof.EnergyBandDecomposition

variable {X : Type*} [MeasurableSpace X] {μ : Measure X} {E : X → ℝ} {f : X → ℂ}
Formal statement
theorem BookProof.ChapterEnergyBoundedEvolution.eLpNorm_evol_sub_self_le {Emax : ℝ} (h : EnergyLimited E μ Emax f) (t : ℝ) :
    eLpNorm (evol E t f - f) 2 μ ≤ ENNReal.ofReal (|t| * Emax) * eLpNorm f 2 μ := by sorry

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