intuition.
eapply compFold_eq.
eapply list_pred_eq.
intuition.
subst.
eauto.
Qed.

Lemma list_pred_app :
forall (A B : Set)(P : A -> B -> Prop)(lsa1 lsa2 : list A)(lsb : list B),
list_pred P (lsa1 ++ lsa2) lsb ->
list_pred P lsa1 (firstn (length lsa1) lsb) *
list_pred P lsa2 (skipn (length lsa1) lsb).