Nicer layout but possibly more bugged.

[helm.git] / helm / software / matita / library / nat / div_and_mod_new.ma

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 2f881b1551a564fb32107ec4c7bcf5f48d07c691..f08a5f94e81f605448c63c511413091462e187f5 100644 (file)
--- 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.