A product comparison between two cyclic linear sums

Proved

WorkbookSource.plus_46295

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

lean-workbooksource-checked

Given $a,b,c \ge 0$ .Prove that: $(a+2b)^2(b+2c)^2(c+2a)^2 \ge 27abc(a+2c)(b+2a)(c+2b)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_46295 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_46295 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : (a + 2 * b) ^ 2 * (b + 2 * c) ^ 2 * (c + 2 * a) ^ 2 ≥ 27 * a * b * c * (a + 2 * c) * (b + 2 * a) * (c + 2 * b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_46295; Apache-2.0

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