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

Lemma list_pred_zip_in :
forall (A B : Set)(P : A -> B -> Prop)(lsa : list A)(lsb : list B),
list_pred P lsa lsb ->
forall a b,
In (a, b) (zip lsa lsb) ->
P a b.