+
+variant times_plus_distr: \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 < sym_times.
+rewrite < sym_times (times n y) z.
+rewrite < H.apply refl_eq.
+qed.
+
+variant assoc_times: \forall n,m,p:nat. (n*m)*p = n*(m*p) \def
+associative_times.