lean_workbook_plus_44420

Proved

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

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

a+b+1\geq 3ab

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44420 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 1 / (a * (b + 1)) + 1 / (b * (a + 1)) = 1) : a + b + 1 ≥ 3 * a * b   :=  by sorry

Source

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

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