lean_workbook_plus_37630

Proved

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

Let $a,b>0$ and $\frac{1}{a(1+b)}+\frac{1}{b(1+a)}=\frac{2}{1+ab}$ . Prove that $a+b\geq2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37630 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a * b ≠ 1) (h : (1 / (a * (1 + b))) + (1 / (b * (1 + a))) = 2 / (1 + a * b)) : a + b ≥ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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