lean_workbook_plus_3937

Proved

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

Let $x, y, z$ are real numbers such that $x<y<z .$ Prove that \n\n

(x-y)^{3}+(y-z)^{3}+(z-x)^{3}>0

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3937 (x y z : ℝ) (hx: x < y) (hy: y < z) : (x - y) ^ 3 + (y - z) ^ 3 + (z - x) ^ 3 > 0   :=  by sorry

Source