lean_workbook_plus_2438

Proved

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

Let $a,b,c$ be positive real numbers. Prove that:\n $a^{3}+b^{3}+c^{3}+ab^{2}+bc^{2}+ca^{2}\ge 2(a^{2}b+b^{2}c+c^{2}a)$ \nAn easy one. I want to a non-SID-CID solution

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2438 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 + a * b^2 + b * c^2 + c * a^2 ≥ 2 * (a^2 * b + b^2 * c + c^2 * a)   :=  by sorry

Source

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

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