induction n; intuition; simpl in *.
inversion H; clear H; subst.
econstructor; intuition.
econstructor.
econstructor; intuition.
inversion H; clear H; subst.
econstructor; intuition.
eapply IHn.
econstructor.
intuition.
intuition.
econstructor; intuition.
Qed.

(* Specifications: *)
Theorem list_pred_nth :
forall n (A B : Set) P (lsa : list A)(lsb : list B) defa defb,
list_pred P lsa lsb ->
P defa defb ->
P (nth n lsa defa) (nth n lsb defb).