A product of squared norms bounds the Vandermonde square

Proved

WorkbookSource.base_33889

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

lean-workbooksource-checked

Let $a,b,c$ are real numbers, show that $2(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge (a-b)^2(b-c)^2(c-a)^2$

Source: InternLM Lean-Workbook, record lean_workbook_33889 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33889 (a b c : ℝ) : 2 * (a^2 + b^2) * (b^2 + c^2) * (c^2 + a^2) ≥ (a - b)^2 * (b - c)^2 * (c - a)^2  :=  by sorry

Source