A seventh-power difference bound under a nonnegative sum

Proved

WorkbookSource.base_45142

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 $x^7 + y^7- x^6y-xy^6+ x^2 + 4x\geq -4$

Source: InternLM Lean-Workbook, record lean_workbook_45142 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_45142 (x y : ℝ) (h : x + y ≥ 0) : x^7 + y^7 - x^6*y - x*y^6 + x^2 + 4*x ≥ -4  :=  by sorry

Source