lean_workbook_plus_18024

Disproved

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

Prove Schur's Inequality in third degree: $a^3 + b^3 + c^3 + 3abc \geq (a+b+c)^3$ for positive real numbers a, b, and c.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18024 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 + 3 * a * b * c ≥ (a + b + c)^3   :=  by sorry

Source