lean_workbook_plus_31275

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} \geq \frac{1}{a+b} +\frac{1}{b+c} +\frac{1}{c+a}

\n\nUse this lemma \n $\frac{1}{a}+\frac{1}{b}\geq \frac{4}{a+b}$ for all $a,b>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31275 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (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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