lean_workbook_plus_81851

Proved

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

For a,b,c>0.Prove that \n $\frac{{{{(a + b + c)}^2}}}{{ab + bc + ca}} \ge \frac{{a + b}}{{a + c}} + \frac{{b + c}}{{b + a}} + \frac{{c + a}}{{c + b}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_81851 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + 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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