A fourth-power sum minus four times the product bounds a squared-difference product

Proved

WorkbookSource.plus_11815

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

lean-workbooksource-checked

Let $a,b,c,d>0$ . Prove that

a^4+b^4+c^4+d^4-4abcd\geq 2(a-b)^2(c-d)^2

Source: InternLM Lean-Workbook, record lean_workbook_plus_11815 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_11815 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : a^4 + b^4 + c^4 + d^4 - 4 * a * b * c * d ≥ 2 * (a - b) ^ 2 * (c - d) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_11815; Apache-2.0

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