lean_workbook_plus_15559

Proved

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

Let $x,y$ be non-negative numbers. Prove that $\frac{1}{x+y+2}+\frac{1}{(x+1)(y+1)}\leq \frac{3}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15559 (x y : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) : (x + y + 2)⁻¹ + (x + 1)⁻¹ * (y + 1)⁻¹ ≤ 3 / 2   :=  by sorry

Source