lean_workbook_plus_6676

Proved

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

Prove that $\frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ca}{c+a}\le \frac{a+b+c}{2}$ , where $a,b,c\in\mathbb{R}^{+}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6676 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * b / (a + b) + b * c / (b + c) + c * a / (c + a)) ≤ (a + b + c) / 2   :=  by sorry

Source

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

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