A cyclic quartic expression with a squared pairwise sum is nonnegative

Proved

WorkbookSource.plus_14687

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

lean-workbooksource-checked

Prove that: $a^4+b^4+c^4+11/2(ab+bc+ca)^2+3(ab^3+bc^3+ca^3)+4(a^3b+b^3c+c^3a) \ge 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_14687 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_14687 (a b c : ℝ) : a^4 + b^4 + c^4 + (11/2)*(a * b + b * c + c * a)^2 + 3 * (a * b^3 + b * c^3 + c * a^3) + 4 * (a^3 * b + b^3 * c + c^3 * a) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_14687; Apache-2.0

View graph