A product of squared pairwise sums bounds three linear factors

Proved

WorkbookSource.base_7483

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

lean-workbooksource-checked

Let $a,b,c >0$ . Prove that

$(a+b)^2(b+c)^2(c+a)^2 \ge abc(2a+b+c)(a+2b+c)(a+b+2c)$

Source: InternLM Lean-Workbook, record lean_workbook_7483 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7483 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b) ^ 2 * (b + c) ^ 2 * (c + a) ^ 2 ≥ a * b * c * (2 * a + b + c) * (a + 2 * b + c) * (a + b + 2 * c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7483; Apache-2.0

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