lean_workbook_plus_2357

Proved

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

Let $a,b,c>0$ . Prove that \n $a,b,c>0\Longrightarrow \frac{a^{2}+b^{2}+c^{2}}{ab+bc+ac}+\frac{1}{2}\geq\sum\frac{a}{b+c}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2357 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2) / (a * b + b * c + a * c) + 1 / 2 ≥ a / (b + c) + b / (c + a) + c / (a + b)   :=  by sorry

Source

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

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