A sixth-degree bound for a squared symmetric cubic sum

Proved

WorkbookSource.base_37001

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

lean-workbooksource-checked

prove that $3(a^2b+ab^2+b^2c+bc^2+c^2a+ca^2)^2\le 4(a^2+b^2+c^2)^3$

Source: InternLM Lean-Workbook, record lean_workbook_37001 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37001 (a b c : ℝ) :
  3 * (a^2 * b + a * b^2 + b^2 * c + b * c^2 + c^2 * a + c * a^2)^2 ≤
  4 * (a^2 + b^2 + c^2)^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_37001; Apache-2.0

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