`BookProof.DampedOscillatorEnergy.dampedEnergy_not_constant_of_damped` {lam omega : ℝ} {x v a : ℝ → ℝ} (hlam : 0 < lam) (hx : ∀ t, HasDerivAt x (v t) t) (hv : ∀ t, HasDerivAt v (a

Proved

BookProof.DampedOscillatorEnergy.dampedEnergy_not_constant_of_damped

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDampedOscillatorEnergy.

BookProof.DampedOscillatorEnergy.dampedEnergy_not_constant_of_damped {lam omega : ℝ} {x v a : ℝ → ℝ} (hlam : 0 < lam) (hx : ∀ t, HasDerivAt x (v t) t) (hv : ∀ t, HasDerivAt v (a t) t) (heq : ∀ t, a t + lam * v t + omega ^ 2 * x t = 0) {t₀ : ℝ} (hmove : v t₀ ≠ 0) : ¬ ∃ E : ℝ, ∀ t, dampedEnergy omega x v t = E

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

Preamble

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



open MeasureTheory

Formal statement

theorem BookProof.DampedOscillatorEnergy.dampedEnergy_not_constant_of_damped {lam omega : ℝ} {x v a : ℝ → ℝ}
    (hlam : 0 < lam) (hx : ∀ t, HasDerivAt x (v t) t) (hv : ∀ t, HasDerivAt v (a t) t)
    (heq : ∀ t, a t + lam * v t + omega ^ 2 * x t = 0) {t₀ : ℝ} (hmove : v t₀ ≠ 0) :
    ¬ ∃ E : ℝ, ∀ t, dampedEnergy omega x v t = E := by sorry

View graph