lean_workbook_plus_9073

Proved

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

Let $a,b\geq0$ real. Prove that \n

\frac{1}{(1+a)^2}+\frac{1}{(1+b)^2} \geq \frac{1}{1+ab}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9073 (a b : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) : (1 / (1 + a) ^ 2 + 1 / (1 + b) ^ 2) ≥ 1 / (1 + a * b)   :=  by sorry

Source