X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Flibrary%2Fnat%2Fprimes1.ma;h=3ec61ee4aff75630b221cff00e359420065f6781;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=55d643262e15b4d4201359a0a6f0c01d515c9871;hpb=4efbd5e75ff51c4104be8c5f35dbabb65f51461f;p=helm.git

diff --git a/helm/matita/library/nat/primes1.ma b/helm/matita/library/nat/primes1.ma
index 55d643262..3ec61ee4a 100644
--- a/helm/matita/library/nat/primes1.ma
+++ b/helm/matita/library/nat/primes1.ma
@@ -16,15 +16,14 @@ set "baseuri" "cic:/matita/nat/primes1".
 
 include "datatypes/constructors.ma".
 include "nat/primes.ma".
-include "nat/exp.ma".
 
 (* p is just an upper bound, acc is an accumulator *)
 let rec n_divides_aux p n m acc \def
-  match (mod n m) with
+  match n \mod m with
   [ O \Rightarrow 
     match p with
       [ O \Rightarrow pair nat nat acc n
-      | (S p) \Rightarrow n_divides_aux p (div n m) m (S acc)]
+      | (S p) \Rightarrow n_divides_aux p (n / m) m (S acc)]
   | (S a) \Rightarrow pair nat nat acc n].
 
 (* n_divides n m = <q,r> if m divides n q times, with remainder r *)
@@ -33,7 +32,7 @@ definition n_divides \def \lambda n,m:nat.n_divides_aux n n m O.
 (*
 theorem n_divides_to_Prop: \forall n,m,p,a. 
   match n_divides_aux p n m a with
-  [ (pair q r) \Rightarrow n = (exp m a)*r].
+  [ (pair q r) \Rightarrow n = m \sup a *r].
 intros.
-apply nat_case (mod n m). *)
+apply nat_case (n \mod m). *)