A polynomial product inequality in three real variables

Proved

WorkbookSource.plus_76073

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

lean-workbooksource-checked

Let $a,b,c\geq 0$ . Prove that: $a^{2}b^{2}c^{2}+2a^{2}b^{2}+2b^{2}c^{2}+2c^{2}a^{2}+a^{2}+b^{2}+c^{2}\geq (abc-1)(ab+bc+ca)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_76073 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_76073 (a b c : ℝ) : a^2 * b^2 * c^2 + 2 * a^2 * b^2 + 2 * b^2 * c^2 + 2 * c^2 * a^2 + a^2 + b^2 + c^2 ≥ (a * b * c - 1) * (a * b + b * c + c * a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_76073; Apache-2.0

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