lean_workbook_plus_28241

Proved

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

Let $x\ge y\ge z>0$ . Prove that $\frac{x}{x+y}+\frac{y}{y+z}+\frac{z}{z+x}\ge \frac{3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_28241 (x y z : ℝ) (h : x ≥ y ∧ y ≥ z ∧ z > 0) :
  x / (x + y) + y / (y + z) + z / (z + x) ≥ 3 / 2   :=  by sorry

Source