A factorial is not congruent to minus two modulo 2003

Proved

WorkbookSource.base_1949

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

lean-workbooksource-checked

How do you show that $1000! ot\equiv -2 \mod 2003$ ?

Source: InternLM Lean-Workbook, record lean_workbook_1949 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1949 : ¬(1000! ≡ -2 [ZMOD 2003])  :=  by sorry

Source