A cyclic quartic expression is nonnegative

Proved

WorkbookSource.plus_39085

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

lean-workbooksource-checked

If a, b, c are real number then: $3(a^4+b^4+c^4)+4(a^3b+b^3c+c^3a)-6abc(a+b+c) \ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_39085 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_39085 (a b c : ℝ) : 3 * (a ^ 4 + b ^ 4 + c ^ 4) + 4 * (a ^ 3 * b + b ^ 3 * c + c ^ 3 * a) - 6 * a * b * c * (a + b + c) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_39085; Apache-2.0

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