A cyclic quartic inequality with coefficient seventeen

Proved

WorkbookSource.base_1181

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

SOS form of: $a^{4} + b^{4} + c^{4} + 17\left(a^{2}b^{2} + b^{2}c^{2} + c^{2}a^{2}\right) \geqq 6\left(a + b + c\right)\left(a^{2}b + b^{2}c + c^{2}a\right)$

Source: InternLM Lean-Workbook, record lean_workbook_1181 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1181 (a b c : ℝ) : a^4 + b^4 + c^4 + 17 * (a^2 * b^2 + b^2 * c^2 + c^2 * a^2) ≥ 6 * (a + b + c) * (a^2 * b + b^2 * c + c^2 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1181; Apache-2.0

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