lean_workbook_plus_26074

Proved

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

Let $a,b>0$ and $\frac{1}{a}+\frac{1}{b}= 1.$ Prove that $\frac{1}{4} \le \frac{1}{a (a+2)} +\frac{1}{b (b +2)} <\frac{1}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_26074 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 1/a + 1/b = 1) : 1/4 ≤ 1/(a * (a + 2)) + 1/(b * (b + 2)) ∧ 1/(a * (a + 2)) + 1/(b * (b + 2)) < 1/3   :=  by sorry

Source

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

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