An eighth-degree binary polynomial inequality

Proved

WorkbookSource.base_1730

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

lean-workbooksource-checked

Prove that $2(x+y)^8+x^4y^4-x^5y^3-x^3y^5\geq 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_1730 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1730 (x y : ℝ) : 2 * (x + y) ^ 8 + x ^ 4 * y ^ 4 - x ^ 5 * y ^ 3 - x ^ 3 * y ^ 5 ≥ 0  :=  by sorry

Source