X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Flibrary%2Fnat%2Fdiv_and_mod.ma;h=d7750e39ad7c03e4424d1d221e50710843d7e87a;hb=e892d4cb9d19305ff88aa1b7dba6e3eaee41fd92;hp=537d3bcf0d11a4207f313f0103d069c1d9d87041;hpb=cd91767a396b7bbc72e6e3ee90a3b758421f935d;p=helm.git

diff --git a/matita/library/nat/div_and_mod.ma b/matita/library/nat/div_and_mod.ma
index 537d3bcf0..d7750e39a 100644
--- a/matita/library/nat/div_and_mod.ma
+++ b/matita/library/nat/div_and_mod.ma
@@ -17,6 +17,7 @@ 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
@@ -331,3 +332,14 @@ 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.
+