`BookProof.DampedOscillatorEnergy.criticallyDamped_energy_not_constant` : ¬ ∃ E : ℝ, ∀ t, dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s)) t = E

Proved

BookProof.DampedOscillatorEnergy.criticallyDamped_energy_not_constant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDampedOscillatorEnergy.

BookProof.DampedOscillatorEnergy.criticallyDamped_energy_not_constant : ¬ ∃ E : ℝ, ∀ t, dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s)) t = E

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

Preamble

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



open MeasureTheory

Formal statement

theorem BookProof.DampedOscillatorEnergy.criticallyDamped_energy_not_constant :
    ¬ ∃ E : ℝ, ∀ t, dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s)) t = E := by sorry

View graph