A sixth-degree inequality with a squared difference correction

Proved

WorkbookSource.base_5888

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

lean-workbooksource-checked

Prove that $(a+b+c)^2(a^2+b^2+c^2)^2 \geq 27abc(a^3+b^3+c^3) + 3(a-b)^2(b-c)^2(c-a)^2$ for non-negative $a, b, c$ .

Source: InternLM Lean-Workbook, record lean_workbook_5888 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5888 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a + b + c) ^ 2 * (a ^ 2 + b ^ 2 + c ^ 2) ^ 2 ≥ 27 * a * b * c * (a ^ 3 + b ^ 3 + c ^ 3) + 3 * (a - b) ^ 2 * (b - c) ^ 2 * (c - a) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5888; Apache-2.0

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