Proof using.
intros.
induction xs; simpl in *; intuition.
break_match.
- simpl in *. intuition; subst; eauto.
break_exists_exists; intuition.
- concludes. break_exists_exists; intuition.
Qed.

Lemma filterMap_app :
forall (f : A -> option B) xs ys,
filterMap f (xs ++ ys) = filterMap f xs ++ filterMap f ys.