induction lsa; intuition; simpl in *.
inversion H; subst; clear H.
econstructor.
inversion H; clear H; subst.
econstructor.
eapply IHlsa; eauto.
trivial.
Qed.

Lemma rel_map_listRepeat : forall (A B : Set)(lsa : list A)(rel : A -> B -> Prop) b,
(forall a, In a lsa -> rel a b) ->
rel_map rel lsa (listRepeat b (length lsa)).