lean_workbook_plus_15662

Proved

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

For $a,b,c \ge 0$ , prove that $\frac{2}{3}( a^2 + b^2 + c^2 )^2 \ge a^3 ( b + c ) + b^3 ( c + a ) + c^3 ( a + b )$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15662 (a b c : ℝ) : (2 / 3) * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 ≥ a ^ 3 * (b + c) + b ^ 3 * (c + a) + c ^ 3 * (a + b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph