A fourth-power bound at zero sum and fixed norm

Proved

WorkbookSource.base_8104

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

lean-workbooksource-checked

Prove that $x^4+y^4+z^4+t^4+u^4 \le 260$ given $x+y+z+t+u=0$ and $x^2+y^2+z^2+t^2+u^2=20$ , where $x,y,z,t,u \in\mathbb{R}$ .

Source: InternLM Lean-Workbook, record lean_workbook_8104 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_8104 (x y z t u : ℝ) (h₁ : x + y + z + t + u = 0) (h₂ : x ^ 2 + y ^ 2 + z ^ 2 + t ^ 2 + u ^ 2 = 20) : x ^ 4 + y ^ 4 + z ^ 4 + t ^ 4 + u ^ 4 ≤ 260  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8104; Apache-2.0

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