lean_workbook_plus_24266

Proved

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

Let $a,b,c>0$ ,prove that: $\frac{ab}{a+2b+c}+\frac{bc}{b+2c+a}+\frac{ca}{c+2a+b} \le \frac{1}{4}(a+b+c).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_24266 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : (a * b / (a + 2 * b + c) + b * c / (b + 2 * c + a) + c * a / (c + 2 * a + b)) ≤ 1 / 4 * (a + b + c)   :=  by sorry

Source

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

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