A cubic-quartic upper bound at squared norm twelve

Proved

WorkbookSource.base_48671

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

lean-workbooksource-checked

For $a,b,c,d \in \mathbb{R}$ that satisfy $a^2+b^2+c^2+d^2=12$ , prove: $4 \left(a^3+b^3+c^3+d^3\right) - \left(a^4+b^4+c^4+d^4 \right) \leq 48$

Source: InternLM Lean-Workbook, record lean_workbook_48671 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_48671 (a b c d : ℝ) (h : a^2 + b^2 + c^2 + d^2 = 12) :
  4 * (a^3 + b^3 + c^3 + d^3) - (a^4 + b^4 + c^4 + d^4) ≤ 48  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48671; Apache-2.0

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