lean_workbook_plus_20524

Proved

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

Show that for positive real numbers $x, y, z$ with $x + y + z = 1$ , the inequality $v \leq \frac{1}{3}$ holds, where $v = xy + yz + zx$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20524 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : x + y + z = 1) : x*y + y*z + z*x ≤ 1/3   :=  by sorry

Source