A two-variable rational expression is at most one half

Proved

WorkbookSource.plus_67249

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

$\frac{(a+b)(1-ab)}{(a^2+1)(b^2+1)} \leqslant \frac{1}{2}.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_67249 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_67249 (a b : ℝ) : (a + b) * (1 - a * b) / (a ^ 2 + 1) / (b ^ 2 + 1) ≤ 1 / 2   :=  by sorry

Source