A cyclic product bound for four real variables

Proved

WorkbookSource.plus_33129

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

lean-workbooksource-checked

Prove that $a^4+b^4+c^4+d^4-4abcd+(a+b)(b+c)(c+d)(d+a) \leqslant (a^2+b^2+c^2+d^2)^2$ given $a,b,c,d\ge 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_33129 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_33129 (a b c d : ℝ) : a^4 + b^4 + c^4 + d^4 - 4 * a * b * c * d + (a + b) * (b + c) * (c + d) * (d + a) ≤ (a^2 + b^2 + c^2 + d^2)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_33129; Apache-2.0

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