lean_workbook_plus_25436

Proved

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

Let $a, b, c$ be positive real numbers. Prove that \n

\frac{1}{2a}+\frac{1}{2b}+\frac{1}{2c}\ge\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_25436 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (2 * a) + 1 / (2 * b) + 1 / (2 * c)) ≥ (1 / (a + b) + 1 / (b + c) + 1 / (c + a))   :=  by sorry

Source

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

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