A quartic and squared-sum bound in four variables

Proved

WorkbookSource.base_34992

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

lean-workbooksource-checked

If $a, b, c, d$ be real and $a^2+b^2+c^2+d^2=4.$ Then $a^4+b^4+c^4+d^4+\frac{4}{3}(a+b+c+d)^2\leq \frac{76}{3}.$

Source: InternLM Lean-Workbook, record lean_workbook_34992 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_34992 (a b c d : ℝ) (h : a^2 + b^2 + c^2 + d^2 = 4) :
  a^4 + b^4 + c^4 + d^4 + (4 / 3) * (a + b + c + d)^2 ≤ (76 / 3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34992; Apache-2.0

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