Two cyclic cubic sums bound a corrected mixed sum

Proved

WorkbookSource.plus_31162

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b$ and $c$ be positive real numbers . Prove that

(a^2b+b^2c+c^2a)(ab^2+bc^2+ca^2)\geq 3abc(a^2(b+c)+b^2(c+a)+c^2(a+b)-3abc)

Source: InternLM Lean-Workbook, record lean_workbook_plus_31162 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_31162 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 * b + b^2 * c + c^2 * a) * (a * b^2 + b * c^2 + c * a^2) ≥ 3 * a * b * c * (a^2 * (b + c) + b^2 * (c + a) + c^2 * (a + b) - 3 * a * b * c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_31162; Apache-2.0

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