induction lsa; destruct lsb; intuition; simpl in *.
econstructor.
inversion H.
inversion H.
inversion H; clear H; subst.
econstructor; intuition.
eauto.
Qed.

(* Specifications: *)
Lemma compMap_spec :
forall (A B C D : Set)(eqdc : EqDec C)(eqdd : EqDec D)(P1 : A -> B -> Prop)(P2 : C -> D -> Prop)(lsa : list A)(lsb : list B)(c1 : A -> Comp C)(c2 : B -> Comp D),
list_pred P1 lsa lsb ->
(forall a b, In a lsa -> In b lsb -> P1 a b -> comp_spec P2 (c1 a) (c2 b)) ->
comp_spec (list_pred P2)
(compMap _ c1 lsa)
(compMap _ c2 lsb).