lean_workbook_plus_2847

Proved

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

Let $a,b>0$ and $\left(a+2b+\dfrac{2}{a+1}\right)\left(b+2a+\dfrac{2}{b+1}\right)= 16$ . Prove that

ab\leq 1

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2847 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : (a + 2 * b + 2 / (a + 1)) * (b + 2 * a + 2 / (b + 1)) = 16) : a * b ≤ 1   :=  by sorry

Source

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

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