From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Fri, 6 Jun 2008 10:21:53 +0000 (+0000)
Subject: cleanup
X-Git-Tag: make_still_working~5075
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=87136b9b874b75fc12df2608edd092a30a9728ff;p=helm.git

cleanup
---

diff --git a/helm/software/matita/library/nat/factorial2.ma b/helm/software/matita/library/nat/factorial2.ma
index bcd228d08..bb6c72aeb 100644
--- a/helm/software/matita/library/nat/factorial2.ma
+++ b/helm/software/matita/library/nat/factorial2.ma
@@ -98,7 +98,7 @@ intro.elim n
 qed.
 
 theorem fact2: \forall n.O < n \to
-(exp (S(S O)) ((S(S O))*n))*(fact n)*(fact n) < fact (S((S(S O))*n)).
+(exp 2 (2*n))*(fact n)*(fact n) < fact (S(2*n)).
 intros.elim H
   [simplify.apply le_S.apply le_n
   |rewrite > times_SSO.
@@ -153,7 +153,7 @@ qed.
 
 (* a slightly better result *)
 theorem fact3: \forall n.O < n \to
-(exp (S(S O)) ((S(S O))*n))*(exp (fact n) (S(S O))) \le (S(S O))*n*fact ((S(S O))*n).
+(exp 2 (2*n))*(exp (fact n) 2) \le 2*n*fact (2*n).
 intros.
 elim H
   [simplify.apply le_n