lean_workbook_plus_51710

Proved

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

Let $a,b$ be positive real numbers. Prove that $\frac{1}{(1+a)^2}+\frac{1}{(1+b)^2}\ge{\frac{1}{1+ab}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_51710 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (1 / (1 + a) ^ 2 + 1 / (1 + b) ^ 2) ≥ 1 / (1 + a * b)   :=  by sorry

Source