A four-variable quartic power-sum inequality at total four

Proved

WorkbookSource.base_7844

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

lean-workbooksource-checked

On the other hand, the following inequality holds for $a+b+c+d=4$ :

13(a^2+b^2+c^2+d^2)^2\ge 12(a^4+b^4+c^4+d^4)+160.

Source: InternLM Lean-Workbook, record lean_workbook_7844 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_7844 (a b c d : ℝ) (h : a + b + c + d = 4) : 13 * (a^2 + b^2 + c^2 + d^2)^2 ≥ 12 * (a^4 + b^4 + c^4 + d^4) + 160  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7844; Apache-2.0

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