A sixth-degree bound involving three differences

Proved

WorkbookSource.base_21519

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

lean-workbooksource-checked

Prove that for any real numbers $a, b, c$ , the following inequality holds:

(a-b)^4(b-c)^2+(b-c)^4(c-a)^2+(c-a)^4(a-b)^2 \geqslant 5(a-b)^2(b-c)^2(c-a)^2.

Source: InternLM Lean-Workbook, record lean_workbook_21519 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_21519 (a b c : ℝ) : (a - b) ^ 4 * (b - c) ^ 2 + (b - c) ^ 4 * (c - a) ^ 2 + (c - a) ^ 4 * (a - b) ^ 2 ≥ 5 * (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_21519; Apache-2.0

View graph