A product inequality for shifted quadratic factors

Proved

WorkbookSource.base_5143

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

lean-workbooksource-checked

Prove that $3(a^2 - a + 1)(c^2 - c + 1) \ge 2(a^2c^2 - ac + 1)$

Source: InternLM Lean-Workbook, record lean_workbook_5143 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5143 (a c : ℝ) : 3 * (a ^ 2 - a + 1) * (c ^ 2 - c + 1) ≥ 2 * (a ^ 2 * c ^ 2 - a * c + 1)  :=  by sorry

Source