lean_workbook_plus_75474

Proved

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

Prove that $(a^2 + b^2+c^2)^2 - 2(a^3b + b^3c+c^3a) \geq 2abc(a+b+c) - (a^2b^2 + b^2c^2 + c^2a^2)$ for all real $a,b,c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_75474 (a b c : ℝ) : (a^2 + b^2 + c^2)^2 - 2 * (a^3 * b + b^3 * c + c^3 * a) ≥ 2 * a * b * c * (a + b + c) - (a^2 * b^2 + b^2 * c^2 + c^2 * a^2)   :=  by sorry

Source

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

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