cleanup

diff --git a/helm/software/matita/library/nat/factorial2.ma b/helm/software/matita/library/nat/factorial2.ma
index bcd228d0801a12f197312637ef7515236b4ba511..bb6c72aebccd7092070199095efb69ea6b279fb3 100644 (file)
--- 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