lean_workbook_plus_73201

Proved

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

If $a,b\geq 1$ prove that $\frac{1}{1+a}+\frac{1}{1+b} \leq \frac{1}{2} + \frac{1}{1+ab}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_73201 (a b : ℝ) (ha : 1 ≤ a) (hb : 1 ≤ b) : (1 / (1 + a) + 1 / (1 + b)) ≤ (1 / 2 + 1 / (1 + a * b))   :=  by sorry

Source