A symmetric four-variable quartic inequality

Proved

WorkbookSource.base_52535

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

lean-workbooksource-checked

Prove that $\frac{17}{8}(a^4+b^4+c^4+d^4-4abcd)\geq(a+b+c+d)(a^3+b^3+c^3+d^3-abc-abd-acd-bcd)$

Source: InternLM Lean-Workbook, record lean_workbook_52535 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_52535 (a b c d : ℝ) : (17 / 8) * (a ^ 4 + b ^ 4 + c ^ 4 + d ^ 4 - 4 * a * b * c * d) ≥ (a + b + c + d) * (a ^ 3 + b ^ 3 + c ^ 3 + d ^ 3 - a * b * c - a * b * d - a * c * d - b * c * d)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52535; Apache-2.0

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