(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
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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.

(* Specifications: *)
Lemma lt_O_fact n : 0 < fact n.
Lemma fact_neq_0 n : fact n <> 0.
Lemma fact_le n m : n <= m -> fact n <= fact m.