intros.
eapply list_pred_app in H0.
rewrite H in H0.
rewrite ?firstn_app, ?skipn_app, ?firstn_ge_all,
?minus_diag, ?firstn_O, ?app_nil_r in * by omega.
firstorder.
Qed.

Theorem compMap_seq_map :
forall (A B C : Set)(eqdc : EqDec C)(ls : list A)(f : A -> B)(c : B -> Comp C),
comp_spec eq
(compMap _ c (map f ls))
(compMap _ (fun x => c (f x)) ls).