lean_workbook_plus_68559

Proved

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

For $a,b\ge 1$ . Show that $\frac{1}{1+a^2}+\frac{1}{1+b^2}\ge \frac{2}{1+ab}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_68559 (a b : ℝ) (ha : 1 ≤ a) (hb : 1 ≤ b) : 1 / (1 + a ^ 2) + 1 / (1 + b ^ 2) ≥ 2 / (1 + a * b)   :=  by sorry

Source