lean_workbook_plus_869

Proved

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

For $a,\ b > 0$ , prove that $\frac {a}{a + 1} + \frac {b}{b + 1}\geq \frac {a + b}{a + b + 1}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_869 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : a / (a + 1) + b / (b + 1) ≥ (a + b) / (a + b + 1)   :=  by sorry

Source