lean_workbook_plus_18225

Proved

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

Prove that $\frac{1}{2 - x} \ge \frac{1 + x^2}{2}$ for $0 \le x < 2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18225 (x : ℝ) (hx : 0 ≤ x ∧ x < 2) : 1 / (2 - x) ≥ (1 + x ^ 2) / 2   :=  by sorry

Source