lean_workbook_plus_76082

Proved

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

Let $a,b$ be positive real numbers . Prove that $\frac{1}{a+b}+\frac{a}{1+b}+\frac{b}{1+a}\ge \frac{3}{2}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76082 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (1 / (a + b) + a / (1 + b) + b / (1 + a)) ≥ 3 / 2   :=  by sorry

Source