+qed.
+
+theorem exp_pi_l: \forall f:nat\to nat.\forall n,m,a:nat.
+(exp a (S n))*pi n f m= pi n (\lambda p.a*(f p)) m.
+intros.elim n.simplify.rewrite < times_n_SO.reflexivity.
+simplify.
+rewrite < H.
+rewrite > assoc_times.
+rewrite > assoc_times in\vdash (? ? ? %).
+apply eq_f.rewrite < assoc_times.
+rewrite < assoc_times.
+apply eq_f2.apply sym_times.reflexivity.
+qed.