lean_workbook_plus_13431

Disproved

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

Prove: $\frac{{x + y}}{{x + y + 1}} > \frac{x}{{x + 1}} + \frac{y}{{y + 1}}$ , for all x, y positive real numbers.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13431 (x y : ℝ) (hx : x > 0) (hy : y > 0) : (x + y) / (x + y + 1) > x / (x + 1) + y / (y + 1)   :=  by sorry

Source