lean_workbook_plus_16489

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

We need to prove $a-(a^3/2) +2a\leqq 2\sqrt{2} <=> (a-\sqrt{2})^2(a+2\sqrt{2}) \geqq 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16489 (a : ℝ) : a - a ^ 3 / 2 + 2 * a ≤ 2 * Real.sqrt 2 ↔ (a - Real.sqrt 2) ^ 2 * (a + 2 * Real.sqrt 2) ≥ 0   :=  by sorry

Source