lean_workbook_plus_4771

Proved

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

Let $a,b,c>0$ . Prove that: $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \geq 3(\frac{1}{a+2b}+\frac{1}{b+2c}+\frac{1}{c+2a})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_4771 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / a + 1 / b + 1 / c ≥ 3 * (1 / (a + 2 * b) + 1 / (b + 2 * c) + 1 / (c + 2 * a))   :=  by sorry

Source

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

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