lean_workbook_plus_78228

Proved

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

Assuming $a,b\ge 1$ as in the original problem statement: $\frac{1}{a^2+1} + \frac{1}{b^2+1}\ge \frac{2}{1+ab}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78228 (a b : ℝ) (ha : 1 ≤ a) (hb : 1 ≤ b) : (a^2 + 1)⁻¹ + (b^2 + 1)⁻¹ ≥ 2 / (1 + a * b)   :=  by sorry

Source