induction ls1; inversion 1; subst; intuition; simpl in *.
comp_simp.
eapply comp_spec_ret; simpl; econstructor.
simpl.
comp_skip.
comp_simp.
comp_skip.
comp_simp.
eapply comp_spec_ret; intuition.
simpl.
econstructor; eauto.
Qed.

(* Specifications: *)
Theorem oc_compMap_eq :
forall (A B C D : Set){eqd : EqDec D}(f1 f2 : A -> OracleComp B C D)(ls : list A) (S : Set){eqds : EqDec S} o (s : S),
(forall s a, comp_spec
eq
((f1 a) _ _ o s)
((f2 a) _ _ o s)) ->
comp_spec
eq
((oc_compMap _ f1 ls) _ _ o s)
((oc_compMap _ f2 ls) _ _ o s).