lean_workbook_plus_6159

Proved

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

With x,y,z>0. Prove that: \n $\frac{1}{4a}+\frac{1}{4b}+\frac{1}{4c}\geq \frac{1}{2a+b+c}+\frac{1}{2b+c+a}+\frac{1}{2c+a+b}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6159 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (4 * a) + 1 / (4 * b) + 1 / (4 * c) ≥ 1 / (2 * a + b + c) + 1 / (2 * b + c + a) + 1 / (2 * c + a + b)   :=  by sorry

Source

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

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