induction lsa; intuition.
simpl in *.
intuition; subst.
econstructor.
unfold compMap in *.
fold compMap in *.
repeat simp_in_support.
econstructor.
eapply H0.
simpl.
intuition.
trivial.
eapply IHlsa.
trivial.
intuition.
Qed.

(* Specifications: *)
Lemma In_zip :
forall (A B : Set)(a : A)( b : B) lsa lsb,
In (a, b) (zip lsa lsb) ->
In a lsa /\ In b lsb.