A symmetric quartic bound involving a triple product

Proved

WorkbookSource.base_33547

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

lean-workbooksource-checked

Prove that for positive real numbers $a, b, c$ :

\frac{a^4+b^4+c^4+5(a^2b^2+b^2c^2+c^2a^2)}{2} \ge 3abc(a+b+c)

Source: InternLM Lean-Workbook, record lean_workbook_33547 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33547 (a b c : ℝ) : (a^4 + b^4 + c^4 + 5 * (a^2 * b^2 + b^2 * c^2 + c^2 * a^2)) / 2 ≥ 3 * a * b * c * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33547; Apache-2.0

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