lean_workbook_plus_16240

Proved

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

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

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16240 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x + y) / (2 * z + x + y) + (y + z) / (2 * x + y + z) + (z + x) / (2 * y + z + x) ≥ 3 / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph