lean_workbook_plus_41516

Proved

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

For non-negative numbers $x$ , $y$ prove that: $\frac{1}{(1+x)^2} + \frac{1}{(1+y)^2} \ge \frac{2}{x^2+y^2+2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41516 (x y : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) : (1 / (1 + x) ^ 2 + 1 / (1 + y) ^ 2) ≥ 2 / (x ^ 2 + y ^ 2 + 2)   :=  by sorry

Source