lean_workbook_plus_774

Proved

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

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

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_774 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : (x + y + 2)⁻¹ - (x + 1)⁻¹ * (y + 1)⁻¹ ≤ 16⁻¹   :=  by sorry

Source