A fourth-power bound for a product of symmetric sums

Proved

WorkbookSource.base_37325

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

lean-workbooksource-checked

$4 \sum a^4 - \sum a^2b^2 \ge (a+b+c)(a^3+b^3+c^3)=\sum a^4+ \sum (sym) a^3b$ $\iff$

Source: InternLM Lean-Workbook, record lean_workbook_37325 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_37325 {a b c : ℝ} :
  4 * (a ^ 4 + b ^ 4 + c ^ 4) - (a ^ 2 * b ^ 2 + b ^ 2 * c ^ 2 + c ^ 2 * a ^ 2) ≥
  (a + b + 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_37325; Apache-2.0

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