`BookProof.DampedOscillatorEnergy.criticallyDamped_hasDerivAt_energy` (t : ℝ) : HasDerivAt (dampedEnergy 1 (fun s => Real.exp (-s)) (fun s => -Real.exp (-s))) (-(2 * (-Real.exp (-t

Proved

BookProof.DampedOscillatorEnergy.criticallyDamped_hasDerivAt_energy

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDampedOscillatorEnergy.

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

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

Preamble

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



open MeasureTheory

Formal statement

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

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