A mixed quartic inequality in two real variables

Proved

WorkbookSource.base_33481

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

lean-workbooksource-checked

Let $x,y$ be real numbers. Prove that

$(x^2 + y^2)^2 + x^3 + y^3 + 4xy^2 + x^2 + y^2\geq 3x^3y + 5x^2y + xy.$

Source: InternLM Lean-Workbook, record lean_workbook_33481 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33481 (x y : ℝ) : (x^2 + y^2)^2 + x^3 + y^3 + 4*x*y^2 + x^2 + y^2 ≥ 3*x^3*y + 5*x^2*y + x*y  :=  by sorry

Source