lean_workbook_plus_14439

Proved

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

Let $a$ , $b$ and $c$ $>0$ such that: $a^2+b^2+c^2 \leq abc$ , show that: $\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{a+c} \leq \frac{1}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14439 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a^2 + b^2 + c^2 ≤ a * b * c) : 1 / (a + b) + 1 / (b + c) + 1 / (a + c) ≤ 1 / 2   :=  by sorry

Source

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

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