lean_workbook_plus_27806

Proved

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

$\bullet$ Use : $\frac{1}{(1+x)^2}+\frac{1}{(1+y)^2}\ge \frac{1}{(1+xy)(1+\frac{x}{y})}+\frac{1}{(1+xy)(1+\frac{y}{x})}=\frac{1}{1+xy}, (x,y>0)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27806 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : 1 / (1 + x) ^ 2 + 1 / (1 + y) ^ 2 ≥ 1 / (1 + x * y)   :=  by sorry

Source