lean_workbook_plus_15122

Proved

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

Given $a, b, c > 0$ satisfy $abc = 1$ . Prove that:\n $\frac{1} {3a + 2b + c} + \frac {1} {3b + 2c + a} + \frac {1} {3c + 2a + b} \leq\ \frac {1} {2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15122 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) : 1 / (3 * a + 2 * b + c) + 1 / (3 * b + 2 * c + a) + 1 / (3 * c + 2 * a + b) ≤ 1 / 2   :=  by sorry

Source

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

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