A symmetric quartic inequality with linear terms

Proved

WorkbookSource.base_81

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

lean-workbooksource-checked

[1]+[2]+[3]+[4] gives $a^{2}b^{2}+b^{2}c^{2}+c^{2}a^{2}+3(a^{2}+b^{2}+c^{2})+6\geq 2(a+b+c)+4(ab+bc+ca)$ .

Source: InternLM Lean-Workbook, record lean_workbook_81 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_81 (a b c : ℝ) : a^2 * b^2 + b^2 * c^2 + c^2 * a^2 + 3 * (a^2 + b^2 + c^2) + 6 ≥ 2 * (a + b + c) + 4 * (a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_81; Apache-2.0

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