A symmetric sixth-degree product comparison

Proved

WorkbookSource.plus_44406

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

lean-workbooksource-checked

For $a,b,c>0$ . Prove that $18\cdot abc\cdot \sum_{cyc} a(a+b)(c+a)\leqq (a+b+c)^3\cdot (a+b)(b+c)(c+a)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_44406 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_44406 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 18 * a * b * c * (a * (a + b) * (a + c) + b * (b + a) * (b + c) + c * (c + a) * (c + b)) ≤ (a + b + c) ^ 3 * (a + b) * (b + c) * (c + a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_44406; Apache-2.0

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