lean_workbook_plus_78657

Proved

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

Prove that $\frac{1}{2a} + \frac{1}{2b} + \frac{1}{2c} \ge \frac{1}{b + c} + \frac{1}{c + a} + \frac{1}{a + b}$ for $a, b, c > 0$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78657 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (2 * a) + 1 / (2 * b) + 1 / (2 * c) ≥ 1 / (b + c) + 1 / (c + a) + 1 / (a + b)   :=  by sorry

Source

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

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