Squared differences bound a Vandermonde product

Proved

WorkbookSource.base_42134

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

lean-workbooksource-checked

Let $a,b,c \in \mathbb{R}$ . Prove that $\sum_{cyc}(a^2-b^2)^2+3\sum_{cyc}(a-b)^2 \ge 6(a-b)(b-c)(c-a)$

Source: InternLM Lean-Workbook, record lean_workbook_42134 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_42134 (a b c : ℝ) :
  (a^2 - b^2)^2 + (b^2 - c^2)^2 + (c^2 - a^2)^2 + 3 * ((a - b)^2 + (b - c)^2 + (c - a)^2) ≥
    6 * (a - b) * (b - c) * (c - a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_42134; Apache-2.0

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