induction lsa1; intuition; simpl in *.
inversion H; clear H; subst.
simpl.
trivial.
inversion H; clear H; subst.
rewrite <- app_comm_cons.
econstructor; eauto.
Qed.

Lemma rel_map_map : forall (A B C : Type)(f : A -> B)(rel : B -> C -> Prop) lsa lsc,
rel_map (fun a c => rel (f a) c) lsa lsc ->
rel_map rel (map f lsa) lsc.