lean_workbook_plus_2973

Proved

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

Prove that for nonnegative a, b, c, $a^{3}+b^{3}+c^{3} \geq a^{2}b+b^{2}c+c^{2}a$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2973 (a b c: ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : a^3 + b^3 + c^3 ≥ a^2 * b + b^2 * c + c^2 * a   :=  by sorry

Source