lean_workbook_plus_1305

Proved

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

Prove that for all positive numbers $x, y, z$ , the following inequality holds: $\sum_{cyc}\frac {x}{y + z} \geq \frac {3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1305 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x / (y + z) + y / (z + x) + z / (x + y)) ≥ 3 / 2   :=  by sorry

Source