lean_workbook_plus_81537

Proved

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

Prove that for any $a,b,c\in\mathbb{R}$ satisfying $a+b+c=1$ , the expression $a^{3}+b^{3}+c^{3}-3abc$ is nonnegative.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81537 {a b c : ℝ} (h : a + b + c = 1) :
  a^3 + b^3 + c^3 - 3 * a * b * c ≥ 0   :=  by sorry

Source