intros A R xs bs cs; elim xs; simpl in |- *; auto.
intros a l H' H'0; inversion H'0; simpl in |- *; auto.
Qed.
Hint Resolve monGoodR.

Lemma subPredExistsL :
forall (A B : Set) (P : Pred A) (S : Pred B) (f : A -> B),
(forall a : A, P a -> S (f a)) ->
forall l : list A, ExistsL A P l -> ExistsL B S (map f l).