A cyclic quartic inequality with coefficients eleven and six

Proved

WorkbookSource.base_54653

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

lean-workbooksource-checked

Prove that for all real numbers $a$ , $b$ , and $c$ , the following inequality holds: $a^4 + b^4 + c^4 + 2(a^3b + b^3c + c^3a) + 11(a^2b^2 + b^2c^2 + c^2a^2) \geq 6(ab^3 + bc^3 + ca^3) + 8abc(a + b + c)$

Source: InternLM Lean-Workbook, record lean_workbook_54653 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_54653 (a b c : ℝ) : a^4 + b^4 + c^4 + 2 * (a^3 * b + b^3 * c + c^3 * a) + 11 * (a^2 * b^2 + b^2 * c^2 + c^2 * a^2) ≥ 6 * (a * b^3 + b * c^3 + c * a^3) + 8 * a * b * c * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_54653; Apache-2.0

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