lean_workbook_plus_1120

Proved

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

Let $a, b,c>0.$ Prove that\n\n

\frac{a+k}{b+c+2k} + \frac{b+k}{c+a+2k} +\frac{c+k}{a+b+2k} \geq \frac{3}{2}

\nWhere $k\geq 0.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1120 (a b c k : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hk : 0 ≤ k) : (a + k) / (b + c + 2 * k) + (b + k) / (c + a + 2 * k) + (c + k) / (a + b + 2 * k) ≥ 3 / 2   :=  by sorry

Source

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

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