induction 1; intuition; simpl in *.
discriminate.
destruct n.
inversion H1; clear H1; subst.
econstructor; intuition.
edestruct IHlist_pred; eauto.
Qed.

(* Specifications: *)
Theorem rndListElem_pred :
forall (A B : Set)(eqda : EqDec A)(eqdb : EqDec B)(P : A -> B -> Prop)(lsa : list A)(lsb : list B),
list_pred P lsa lsb ->
comp_spec (fun a b =>
match a with
| None => b = None
| Some a' => exists b', b = Some b' /\ P a' b'
end) (rndListElem _ lsa) (rndListElem _ lsb).