lean_workbook_plus_4094

Proved

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

Let $a,\ b,\ c$ be real numbers. Prove that $|x|\leq\frac{1}{2}x^{2}+\frac{1}{2}\Longleftrightarrow (|x|-1)^{2}\geq 0$ ,

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4094 (x : ℝ) : |x| ≤ 1/2 * x^2 + 1/2 ↔ (|x| - 1)^2 ≥ 0   :=  by sorry

Source