intros.
split; induction l1; intros.
inv H. destruct l2; inv H0. auto.
split. auto. simpl in H2. inv H2.
constructor; auto.
split. inv H. constructor; auto. apply IHl1 in H3.
intuition.
inv H. apply IHl1 in H3. intuition.
simpl. intuition.
simpl. constructor.
destruct H. inv H. auto.
apply IHl1. intuition.
inv H0; auto.
Qed.

Lemma Forall_map:
forall {A B} (f: B -> Prop) (g: A -> B) al,
Forall f (map g al) <-> Forall (Basics.compose f g) al.