induction 1; intuition; simpl.
eapply comp_spec_eq_refl.
eapply comp_spec_seq; intuition.
subst.
intuition.
Qed.

Lemma list_pred_zip_l :
forall (A B: Set)(lsa : list A)(lsb : list B)(P : A -> B -> Prop),
list_pred P lsa lsb ->
forall (C : Set)(lsc : list C)(P1 : A -> C -> Prop)(P2 : B -> C -> Prop),
list_pred P1 lsa lsc ->
list_pred P2 lsb lsc ->
list_pred (fun (p : A * B) c => P (fst p) (snd p) /\ P1 (fst p) c /\ P2 (snd p) c) (zip lsa lsb) lsc.