lean_workbook_plus_79225

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $\frac{1}{x+y+3}-\frac{1}{(x+1)(y+2)}\le\frac{1}{16}$ for nonnegative numbers $x$ and $y$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79225 (x y : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) : (x + y + 3)⁻¹ - (x + 1)⁻¹ * (y + 2)⁻¹ ≤ 16⁻¹   :=  by sorry

Source