lean_workbook_plus_53946

Proved

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

Let $a$ and $b$ be real numbers with $0\le a, b\le 1$ . Prove that

\frac{a}{b + 1}+\frac{b}{a + 1}\le 1

When does equality holds?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_53946 (a b : ℝ) (ha : 0 ≤ a ∧ a ≤ 1) (hb : 0 ≤ b ∧ b ≤ 1) : a / (b + 1) + b / (a + 1) ≤ 1   :=  by sorry

Source