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-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(*i $Id: Factorial.v,v 1.1.2.1 2004/07/16 19:31:24 herbelin Exp $ i*)
-
-Require Plus.
-Require Mult.
-Require Lt.
-V7only [Import nat_scope.].
-Open Local Scope nat_scope.
-
-(** Factorial *)
-
-Fixpoint fact [n:nat]:nat:=
-  Cases n of
-     O     => (S O)
-    |(S n) => (mult (S n) (fact n))
-  end.
-
-Arguments Scope fact [ nat_scope ].
-
-Lemma lt_O_fact : (n:nat)(lt O (fact n)).
-Proof.
-Induction n; Unfold lt; Simpl; Auto with arith.
-Qed.
-
-Lemma fact_neq_0:(n:nat)~(fact n)=O.
-Proof.
-Intro.
-Apply sym_not_eq.
-Apply lt_O_neq.
-Apply lt_O_fact.
-Qed.
-
-Lemma fact_growing : (n,m:nat) (le n m) -> (le (fact n) (fact m)).
-Proof.
-NewInduction 1.
-Apply le_n.
-Assert (le (mult (S O) (fact n)) (mult (S m) (fact m))).
-Apply le_mult_mult.
-Apply lt_le_S; Apply lt_O_Sn.
-Assumption.
-Simpl (mult (S O) (fact n)) in H0.
-Rewrite <- plus_n_O in H0.
-Assumption.
-Qed.