X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Fnat%2Fdiv_and_mod_new.ma;h=f08a5f94e81f605448c63c511413091462e187f5;hb=0ac6c9a8f9cb3206002178edcf2dfa761c7a94ef;hp=2f881b1551a564fb32107ec4c7bcf5f48d07c691;hpb=a180bddcd4a8f35de3d7292162ba05d0077723aa;p=helm.git

diff --git a/helm/software/matita/library/nat/div_and_mod_new.ma b/helm/software/matita/library/nat/div_and_mod_new.ma
index 2f881b155..f08a5f94e 100644
--- a/helm/software/matita/library/nat/div_and_mod_new.ma
+++ b/helm/software/matita/library/nat/div_and_mod_new.ma
@@ -358,3 +358,12 @@ let rec n_divides_aux p n m acc \def
 
 (* n_divides n m = <q,r> if m divides n q times, with remainder r *)
 definition n_divides \def \lambda n,m:nat.n_divides_aux n n m O.
+
+(*a simple variant of div_times theorem *)
+theorem div_times_ltO: \forall a,b:nat. O \lt b \to
+a*b/b = a.
+intros.
+rewrite > sym_times.
+rewrite > (S_pred b H).
+apply div_times.
+qed.