A sixth-power bound for the Vandermonde square

Proved

WorkbookSource.base_26943

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

lean-workbooksource-checked

Let $a,b,c$ Be real numbers. Prove that $2a^6+2b^6+2c^6-6a^2b^2c^2 \geqslant (a-b)^2(b-c)^2(c-a)^2$

Source: InternLM Lean-Workbook, record lean_workbook_26943 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_26943 (a b c : ℝ) : 2 * a ^ 6 + 2 * b ^ 6 + 2 * c ^ 6 - 6 * a ^ 2 * b ^ 2 * c ^ 2 ≥ (a - b) ^ 2 * (b - c) ^ 2 * (c - a) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_26943; Apache-2.0

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