`BookProof.DampedOscillatorEnergy.criticallyDamped_energy` (t : ℝ) : dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s)) t = Real.exp (-t) ^ 2

Proved

BookProof.DampedOscillatorEnergy.criticallyDamped_energy

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDampedOscillatorEnergy.

BookProof.DampedOscillatorEnergy.criticallyDamped_energy (t : ℝ) : dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s)) t = Real.exp (-t) ^ 2

Formalization note: Lean 4 identifier BookProof.DampedOscillatorEnergy.criticallyDamped_energy.

Preamble

-- Generated from ChapterDampedOscillatorEnergy.lean — theorem BookProof.DampedOscillatorEnergy.criticallyDamped_energy
import Mathlib
import Definitions.Def_ChapterDampedOscillatorEnergy
open BookProof.DampedOscillatorEnergy



open MeasureTheory

Formal statement

theorem BookProof.DampedOscillatorEnergy.criticallyDamped_energy (t : ℝ) :
    dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s)) t
      = Real.exp (-t) ^ 2 := by sorry

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