A fifth-power difference bound under a nonnegative sum

Proved

WorkbookSource.base_10663

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

lean-workbooksource-checked

Let $x, y$ are real numbers such that $x + y \geq 0.$ Prove that $x ^ 5 + y ^ 5-x ^ 4y-xy ^ 4 + x ^ 2 + 4x + 7\geq 3$

Source: InternLM Lean-Workbook, record lean_workbook_10663 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10663 (x y : ℝ) (h : x + y ≥ 0) :
  x ^ 5 + y ^ 5 - x ^ 4 * y - x * y ^ 4 + x ^ 2 + 4 * x + 7 ≥ 3  :=  by sorry

Source