lean_workbook_plus_66666

Proved

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

Let $a, b, c> 0$ . Prove: $2+\frac{a^2+b^2+c^2}{ab+bc+ca}\geq \frac{a+b}{a+c}+\frac{b+c}{b+a}+\frac{c+a}{c+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_66666 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 + (a ^ 2 + b ^ 2 + c ^ 2) / (a * b + b * c + c * a) ≥ (a + b) / (a + c) + (b + c) / (b + a) + (c + a) / (c + b)   :=  by sorry

Source

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

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