induction lsa; intuition; simpl in *.
econstructor.
econstructor; eauto.
Qed.

Lemma rel_map_app : forall (A B : Type)(rel : A -> B -> Prop)(lsa1 lsa2 : list A)(lsb1 lsb2 : list B),
rel_map rel lsa1 lsb1 ->
rel_map rel lsa2 lsb2 ->
rel_map rel (lsa1 ++ lsa2) (lsb1 ++ lsb2).