lean_workbook_plus_8949

Proved

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

Let $a, b \geq 1$ . Prove that $\frac{1}{1+a^2}+\frac{1}{1+b^2}\geq \frac{2}{1+ab}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8949 (a b : ℝ) (ha : 1 ≤ a) (hb : 1 ≤ b) : (1 / (1 + a^2) + 1 / (1 + b^2)) ≥ 2 / (1 + a * b)   :=  by sorry

Source