added hmysql

[helm.git] / helm / matita / library / nat / times.ma

diff --git a/helm/matita/library/nat/times.ma b/helm/matita/library/nat/times.ma
index 2707c2ba1cdd8ff08a0404fa40de9f714390542c..8c53a56c8adfb7872ffa6a846525edf58069cc60 100644 (file)
--- a/helm/matita/library/nat/times.ma
+++ b/helm/matita/library/nat/times.ma
@@ -43,7 +43,7 @@ reflexivity.
 apply assoc_plus.
 qed.
 
-theorem times_n_SO : \forall n:nat. eq nat n (times n (S O)).
+theorem times_n_SO : \forall n:nat. n = n * S O.
 intros.
 rewrite < times_n_Sm.
 rewrite < times_n_O.
@@ -70,14 +70,14 @@ apply eq_f.rewrite < assoc_plus. rewrite < sym_plus ? z.
 rewrite > assoc_plus.reflexivity.
 qed.
 
-variant times_plus_distr: \forall n,m,p:nat. n*(m+p) = n*m + n*p
+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.
 simplify.intros.
 elim x.simplify.apply refl_eq.
 simplify.rewrite < sym_times.
-rewrite > times_plus_distr.
+rewrite > distr_times_plus.
 rewrite < sym_times.
 rewrite < sym_times (times n y) z.
 rewrite < H.apply refl_eq.