lean_workbook_plus_12604

Disproved

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

Derive the inequality $a^3+b^3+c^3\geq 3abc$ using the identity $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12604 : ∀ a b c : ℝ, a^3 + b^3 + c^3 ≥ 3 * a * b * c   :=  by sorry

Source