Proof using.
induction xs; intros; simpl in *; intuition.
rewrite H; auto.
Qed.

Lemma filterMap_NoDup_inj :
forall (f : A -> option B) l,
(forall x1 x2 y,
f x1 = Some y ->
f x2 = Some y ->
x1 = x2) ->
NoDup l ->
NoDup (filterMap f l).