intros A P xs; elim xs; simpl in |- *; auto.
Qed.
Hint Resolve monExistsL1.

(* Specifications: *)
Lemma monExistsL :
forall (A : Set) (P : Pred A) (xs bs cs : list A),
ExistsL A P (xs ++ bs) -> ExistsL A P (xs ++ cs ++ bs).