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.