A strengthened sixth-degree Schur-type inequality

Proved

WorkbookSource.plus_89

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

For $a,b,c>0$ , prove or disprove: $\sum{a^4{\left(a-b\right)}{\left(a-c\right)}}\ge5\prod{{\left(b-c\right)}^2}\text.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_89 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_89 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 * (a - b) * (a - c) + b^4 * (b - a) * (b - c) + c^4 * (c - a) * (c - b) ≥ 5 * (b - c)^2 * (c - a)^2 * (a - b)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_89; Apache-2.0

View graph