A cyclic cubic inequality involving a triple product

Proved

WorkbookSource.base_30428

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove: $\sum a^3+ 3\sum ac^2 \geq 3\sum a^2c+3abc$ , given $a,b,c >0$ .

Source: InternLM Lean-Workbook, record lean_workbook_30428 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30428 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a ^ 3 + b ^ 3 + c ^ 3 + 3 * (a * c ^ 2 + b * a ^ 2 + c * b ^ 2) ≥ 3 * (a ^ 2 * c + b ^ 2 * a + c ^ 2 * b) + 3 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30428; Apache-2.0

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