A cyclic quartic correction to the squared sum of squares

Proved

WorkbookSource.base_18619

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers, prove that $(a^2+b^2+c^2)^2 +3(a^3b+b^3c+c^3a)\geq 6abc(a+b+c).$

Source: InternLM Lean-Workbook, record lean_workbook_18619 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18619 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2)^2 + 3 * (a^3 * b + b^3 * c + c^3 * a) ≥ 6 * a * b * c * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18619; Apache-2.0

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