induction l.
split...
intros.
inversion H0.
destruct IHl.
split; simpl; intros.
rewrite H1...
destruct H2.
subst.
destruct (p x)...
discriminate.
apply H0...
destruct (p a)...
discriminate.
Qed.

(* Specifications: *)
Lemma incl_map X Y (f: X -> Y) (a b: list X): incl a b -> incl (map f a) (map f b).
Proof with auto.