lean_workbook_plus_16666

Proved

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

For $a,b,c\ge0$ , prove that $\frac23(a^2+b^2+c^2)^2\ge{a^3(b+c)+b^3(a+c)+c^3(a+b)}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16666 (a b c : ℝ) : (2 / 3) * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 ≥ a ^ 3 * (b + c) + b ^ 3 * (a + c) + c ^ 3 * (a + b)   :=  by sorry

Source

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

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