A symmetric cubic inequality

Proved

WorkbookSource.problem_52163

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c \ge 0$ . prove that

$abc + 5(a + b + c)^3 \ge 17(a + b)(b + c)(c + a)$

Source: InternLM Lean-Workbook, record lean_workbook_52163 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_52163 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : a * b * c + 5 * (a + b + c) ^ 3 ≥ 17 * (a + b) * (b + c) * (c + a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52163; Apache-2.0

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