X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fdiv_and_mod.ma;h=538515a8cc806003287340ef9d1299b4625a17a0;hb=54551ce5acf37f04972291e774d14371a671a8c7;hp=0323b18fb17849949b5ce4a49e3b33476f14fcec;hpb=6db38e3d8e4083765f2fce40c7845c9827b9afd0;p=helm.git

diff --git a/helm/software/matita/library/nat/div_and_mod.ma b/helm/software/matita/library/nat/div_and_mod.ma
index 0323b18fb..538515a8c 100644
--- a/helm/software/matita/library/nat/div_and_mod.ma
+++ b/helm/software/matita/library/nat/div_and_mod.ma
@@ -12,12 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-set "baseuri" "cic:/matita/nat/div_and_mod".
-
 include "datatypes/constructors.ma".
 include "nat/minus.ma".
 
-
 let rec mod_aux p m n: nat \def
 match (leb m n) with
 [ true \Rightarrow m
@@ -223,6 +220,7 @@ apply (div_mod_spec_to_eq2 (q*m+r) m ((q*m+r)/ m) ((q*m+r) \mod m) q r)
   |apply div_mod_spec_intro[assumption|reflexivity]
   ]
 qed.
+
 (* some properties of div and mod *)
 theorem div_times: \forall n,m:nat. ((S n)*m) / (S n) = m.
 intros.
@@ -312,19 +310,6 @@ rewrite > (div_mod ? (S O)) in \vdash (? ? ? %)
   ]
 qed.
 
-theorem le_div: \forall n,m. O < n \to m/n \le m.
-intros.
-rewrite > (div_mod m n) in \vdash (? ? %)
-  [apply (trans_le ? (m/n*n))
-    [rewrite > times_n_SO in \vdash (? % ?).
-     apply le_times
-      [apply le_n|assumption]
-    |apply le_plus_n_r
-    ]
-  |assumption
-  ]
-qed.
-
 theorem or_div_mod: \forall n,q. O < q \to
 ((S (n \mod q)=q) \land S n = (S (div n q)) * q \lor
 ((S (n \mod q)<q) \land S n= (div n q) * q + S (n\mod q))).
@@ -395,6 +380,7 @@ qed.
 variant inj_times_l1:\forall n. O < n \to \forall p,q:nat.p*n = q*n \to p=q
 \def lt_O_to_injective_times_l.
 
+      
 (* n_divides computes the pair (div,mod) *)
 
 (* p is just an upper bound, acc is an accumulator *)