A factorial bound with a power of two

Proved

WorkbookSource.base_56627

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

lean-workbooksource-checked

Prove that $2^{2002} \cdot 2002! < 2003^{2002}$ .

Source: InternLM Lean-Workbook, record lean_workbook_56627 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_56627 : (2:ℝ) ^ 2002 * 2002! < 2003 ^ 2002  :=  by sorry

Source