Prove2Me

A sixth-degree Schur-type bound with a difference correction

Proved
WorkbookSource.plus_18871

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

lean-workbooksource-checked

For all nonnegative reals x,y,z, x,y,z, prove that x2(x2−y2)(x2−z2)+y2(y2−z2)(y2−x2)+z2(z2−x2)(z2−y2)≥8(y−z)2(z−x)2(x−y)2. x^2(x^2 - y^2)(x^2 - z^2) + y^2(y^2 - z^2)(y^2 - x^2) + z^2(z^2 - x^2)(z^2 - y^2)\geq 8(y - z)^2(z - x)^2(x - y)^2.

Source: InternLM Lean-Workbook, record lean_workbook_plus_18871 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_18871 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : x^2 * (x^2 - y^2) * (x^2 - z^2) + y^2 * (y^2 - z^2) * (y^2 - x^2) + z^2 * (z^2 - x^2) * (z^2 - y^2) ≥ 8 * (y - z)^2 * (z - x)^2 * (x - y)^2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_18871; Apache-2.0

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