A four-variable fourth-power inequality with a cyclic difference product

Proved

WorkbookSource.plus_62202

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

lean-workbooksource-checked

Let $a$ , $b$ , $c$ $d$ non-negative real numbers. Prove that: $a^4+b^4+c^4+d^4+2(a-b)(b-c)(c-d)(d-a) \geq 4abcd$

Source: InternLM Lean-Workbook, record lean_workbook_plus_62202 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_62202 (a b c d : ℝ) : a^4 + b^4 + c^4 + d^4 + 2 * (a - b) * (b - c) * (c - d) * (d - a) ≥ 4 * a * b * c * d   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_62202; Apache-2.0

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