A sixth-degree bound on a product of three quadratic differences

Proved

WorkbookSource.base_7388

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers. Prove the inequality

8(a^2-bc)(b^2-ca)(c^2-ab) \leqslant (a^2+b^2+c^2)^3

Source: InternLM Lean-Workbook, record lean_workbook_7388 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7388 (a b c : ℝ) : 8 * (a^2 - b * c) * (b^2 - c * a) * (c^2 - a * b) ≤ (a^2 + b^2 + c^2)^3  :=  by sorry

Source