lean_workbook_plus_21709

Proved

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

Let $a,b>0$ and $a^2+b^2\geq 2.$ Prove that

\frac{a}{a^2+b}+\frac{b}{b^2+a}\leq1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21709 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a^2 + b^2 ≥ 2) : a / (a^2 + b) + b / (b^2 + a) ≤ 1   :=  by sorry

Source