Prove2Me

A product of three quadratics bounds a squared triple product difference

Proved
WorkbookSource.base_6442

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

lean-workbooksource-checked

If a,b,c≥0a,b,c\ge 0 , then

2(a2−a+1)(b2−b+1)(c2−c+1)≥(abc−1)2.2(a^2-a+1)(b^2-b+1)(c^2-c+1)\ge (abc-1)^2.

Source: InternLM Lean-Workbook, record lean_workbook_6442 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_6442 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : 2 * (a^2 - a + 1) * (b^2 - b + 1) * (c^2 - c + 1) ≥ (a * b * c - 1)^2  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6442; Apache-2.0

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