induction lsa; destruct lsb; intuition; simpl in *; try omega.
econstructor.
econstructor;
intuition.
Qed.

Lemma list_pred_length_eq :
forall (A B : Set)(lsa : list A)(lsb : list B)(P : A -> B -> Prop),
list_pred P lsa lsb ->
length lsa = length lsb.