lean_workbook_plus_24566

Proved

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

The following inequality is also true.\n\nLet $a$ , $b$ and $c$ be positive numbers such that $a+b+c\geq3$ . Prove that:\n\n

5abc+4\geq\frac{27}{a^3+b^3+c^3}

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_24566 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (hab : a + b + c >= 3) : 5 * a * b * c + 4 ≥ 27 / (a ^ 3 + b ^ 3 + c ^ 3)   :=  by sorry

Source

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

View graph