lean_workbook_plus_79307

Proved

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

For $a,b,c\ge 0$ prove that : \n\n $a^3b^2+b^3a^2+b^3c^2+c^3b^2+c^3a^2+a^3c^2\ge abc (a^2+b^2+c^2+ab+bc+ca)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79307 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : a^3 * b^2 + b^3 * a^2 + b^3 * c^2 + c^3 * b^2 + c^3 * a^2 + a^3 * c^2 ≥ a * b * c * (a^2 + b^2 + c^2 + a * b + b * c + c * a)   :=  by sorry

Source

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

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