A sharp comparison of two binary quartic forms

Proved

WorkbookSource.base_389

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

lean-workbooksource-checked

Prove that $8(x^4+x^3y+xy^3+y^4) \leq 9(x^4+2x^2y^2+y^4)$ for all real numbers $x,y$ .

Source: InternLM Lean-Workbook, record lean_workbook_389 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_389 (x y : ℝ) : 8 * (x ^ 4 + x ^ 3 * y + x * y ^ 3 + y ^ 4) ≤ 9 * (x ^ 4 + 2 * x ^ 2 * y ^ 2 + y ^ 4)  :=  by sorry

Source