lean_workbook_plus_42019

Proved

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

Given $a, b, c >0$ . Prove that $\frac{1}{a+b} + \frac{1}{b+c} + \frac{1}{c+a} \le \frac{1}{2} (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_42019 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (a + b) + 1 / (b + c) + 1 / (c + a) ≤ 1 / 2 * (1 / a + 1 / b + 1 / c)   :=  by sorry

Source

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

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