lean_workbook_plus_2800

Proved

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

Prove the inequality $\frac{(a+b)(b+c)(c+a)}{8}\leq\frac{(a+b+c)^3}{27}$ where $a, b, c > 1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2800 (a b c : ℝ) (ha : 1 < a) (hb : 1 < b) (hc : 1 < c) : (a + b) * (b + c) * (c + a) / 8 ≤ (a + b + c) ^ 3 / 27   :=  by sorry

Source

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

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