Added a property.

diff --git a/helm/software/matita/library/nat/times.ma b/helm/software/matita/library/nat/times.ma
index 57dc60c6f2a071b5e25400161da998fa88f12763..32fbc7651caf25f77ee7e97e149e28336dc99a7c 100644 (file)
--- a/helm/software/matita/library/nat/times.ma
+++ b/helm/software/matita/library/nat/times.ma
@@ -21,6 +21,11 @@ let rec times n m \def
 
 interpretation "natural times" 'times x y = (cic:/matita/nat/times/times.con x y).
 
+theorem times_Sn_m:
+\forall n,m:nat. m+n*m = S n*m.
+intros. reflexivity.
+qed.
+
 theorem times_n_O: \forall n:nat. O = n*O.
 intros.elim n.
 simplify.reflexivity.
@@ -90,6 +95,7 @@ theorem symmetric_times : symmetric nat times.
 unfold symmetric.
 intros.elim x.
 simplify.apply times_n_O.
+(* applyS times_n_Sm. *) 
 simplify.rewrite > H.apply times_n_Sm.
 qed.
 
@@ -109,8 +115,9 @@ variant distr_times_plus: \forall n,m,p:nat. n*(m+p) = n*m + n*p
 \def distributive_times_plus.
 
 theorem associative_times: associative nat times.
-unfold associative.intros.
-elim x.simplify.apply refl_eq.
+unfold associative.
+intros.
+elim x. simplify.apply refl_eq. 
 simplify.rewrite < sym_times.
 rewrite > distr_times_plus.
 rewrite < sym_times.
@@ -120,3 +127,8 @@ qed.
 
 variant assoc_times: \forall n,m,p:nat. (n*m)*p = n*(m*p) \def
 associative_times.
+
+lemma times_times: ∀x,y,z. x*(y*z) = y*(x*z).
+intros.autobatch paramodulation.
+qed.
+