lean_workbook_plus_25787

Proved

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

Let $a,b$ be positive real numbers . Prove that $\frac{1}{2a}+\frac{1}{b+1}+\frac{1}{ab+b}\ge \frac{3}{ab+1}.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25787 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : 1 / (2 * a) + 1 / (b + 1) + 1 / (a * b + b) ≥ 3 / (a * b + 1)   :=  by sorry

Source