A seventh-power sum bound under zero sum

Proved

WorkbookSource.base_35906

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

lean-workbooksource-checked

Let $a,b,c,d$ be any real numbers such that $a+b+c+d=0$ , prove that $1296(a^7+b^7+c^7+d^7)^2\le637(a^2+b^2+c^2+d^2)^7$

Source: InternLM Lean-Workbook, record lean_workbook_35906 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_35906 (a b c d : ℝ) (h : a + b + c + d = 0) :
  1296 * (a^7 + b^7 + c^7 + d^7)^2 ≤ 637 * (a^2 + b^2 + c^2 + d^2)^7  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35906; Apache-2.0

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