A two-variable quartic inequality with a shifted cubic factor

Proved

WorkbookSource.base_35723

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

lean-workbooksource-checked

If $x,\,y$ are real numbers, then $xy(x^2+y^2) \leqslant 2+\frac12 (x+y-2) (x+y)^3.$

Source: InternLM Lean-Workbook, record lean_workbook_35723 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_35723 (x y : ℝ) : x * y * (x ^ 2 + y ^ 2) ≤ 2 + 1 / 2 * (x + y - 2) * (x + y) ^ 3  :=  by sorry

Source