Fixpoint filterMap {A B} (f : A -> option B) (l : list A) : list B :=
  match l with
    | [] => []
    | x :: xs => match f x with
                   | None => filterMap f xs
                   | Some y => y :: filterMap f xs
                 end
  end.

Lemma filterMap_ext : forall (f g : A -> option B) l, (forall x, f x = g x) -> filterMap f l = filterMap g l.