A product comparison between cyclic linear and quadratic factors

Proved

WorkbookSource.base_28904

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

lean-workbooksource-checked

Prove that for all $a,b,c>0$ we have $abc(a+2c)(b+2a)(c+2b)\le(a^{2}+2bc)(b^{2}+2ca)(c^{2}+2ab)$

Source: InternLM Lean-Workbook, record lean_workbook_28904 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_28904 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a * b * c * (a + 2 * c) * (b + 2 * a) * (c + 2 * b) ≤ (a ^ 2 + 2 * b * c) * (b ^ 2 + 2 * c * a) * (c ^ 2 + 2 * a * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_28904; Apache-2.0

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