(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Local Open Scope nat_scope.
(** Factorial *)
Fixpoint fact (n:nat) : nat :=
match n with
| O => 1
| S n => S n * fact n
end.
Arguments fact n%nat.

Lemma lt_O_fact n : 0 < fact n.