A cyclic quartic sum times the total bounds a symmetric product

Proved

WorkbookSource.base_56810

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that: $(\sum a^{3}b)(\sum a)\geq 3abc(\sum a^{2})$

Source: InternLM Lean-Workbook, record lean_workbook_56810 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_56810 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 * b + b^3 * c + c^3 * a) * (a + b + c) ≥ 3 * a * b * c * (a^2 + b^2 + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_56810; Apache-2.0

View graph