A cubic power of the sum of squares bounds three symmetric sums

Proved

WorkbookSource.base_9695

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

lean-workbooksource-checked

If $a,b,c >0$ , prove that $(a^2+b^2+c^2)^3 \geq (a+b+c)(ab+bc+ca)(a^3+b^3+c^3)$

Source: InternLM Lean-Workbook, record lean_workbook_9695 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9695 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + b^2 + c^2)^3 ≥ (a + b + c) * (a * b + b * c + a * c) * (a^3 + b^3 + c^3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9695; Apache-2.0

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