A symmetric quartic bound with a triple-product correction

Proved

WorkbookSource.base_14253

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $3(a^4+b^4+c^4)+3abc(a+b+c)\geq ab(a^2+b^2)+bc(b^2+c^2)+ca(c^2+a^2)$ .

Source: InternLM Lean-Workbook, record lean_workbook_14253 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_14253 (a b c : ℝ) : 3 * (a ^ 4 + b ^ 4 + c ^ 4) + 3 * a * b * c * (a + b + c) ≥ a * b * (a ^ 2 + b ^ 2) + b * c * (b ^ 2 + c ^ 2) + c * a * (c ^ 2 + a ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_14253; Apache-2.0

View graph