lean_workbook_plus_23983

Proved

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

Let $a,b,c>0$ and $abc=1$ . Prove that \n

\dfrac{1}{9}-\dfrac{a}{(a+2)^2} \geq \dfrac{1}{9\left(a^2+a+1\right)}-\dfrac{1}{27}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_23983 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 1 / 9 - a / (a + 2) ^ 2 ≥ 1 / (9 * (a ^ 2 + a + 1)) - 1 / 27   :=  by sorry

Source

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

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