lean_workbook_plus_76682

Proved

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

Let $a,b,c$ be sides of triangle. Prove that $\dfrac{(a+b)(b+c)(c+a)}{8} \ge \dfrac{(2a+b)(2b+c)(2c+a)}{27}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76682 (a b c : ℝ) (hx: a > 0 ∧ b > 0 ∧ c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : (a + b) * (b + c) * (c + a) / 8 ≥ (2 * a + b) * (2 * b + c) * (2 * c + a) / 27   :=  by sorry

Source

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

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