induction lsa; destruct lsb; intuition.
simpl.
eapply comp_spec_ret; intuition.
simpl in *.
discriminate.
simpl in *.
discriminate.
simpl.
eapply comp_spec_seq; intuition.
eapply H1; eauto.
eapply IHlsa; eauto.
Qed.

Lemma compMap_support_app :
forall (A B : Set)(eqd : EqDec B)(c : A -> Comp B)(lsa1 lsa2 : list A)(lsb1 lsb2 : list B),
In lsb1 (getSupport (compMap _ c lsa1)) ->
In lsb2 (getSupport (compMap _ c lsa2)) ->
In (lsb1 ++ lsb2) (getSupport (compMap _ c (lsa1 ++ lsa2))).