A sixth-degree inequality involving squared pairwise sums

Proved

WorkbookSource.base_3963

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

lean-workbooksource-checked

If $a,b,c > 0$ prove that: $a^2b^2(a + b)^2 + b^2c^2(b + c)^2 + c^2a^2(c + a)^2 + 6a^2b^2c^2 \geq 2abc(a + b + c)(a^2 + b^2 + c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_3963 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3963 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 * b^2 * (a + b)^2 + b^2 * c^2 * (b + c)^2 + c^2 * a^2 * (c + a)^2 + 6 * a^2 * b^2 * c^2 ≥ 2 * a * b * c * (a + b + c) * (a^2 + b^2 + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3963; Apache-2.0

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