(** * Other list functions *)
Fixpoint listoption_inv {A} (l : list (option A)) : list A :=
match l with
| Some x :: l => x :: listoption_inv l
| None :: l => listoption_inv l
| nil => nil
end.

(* Specifications: *)
Lemma map_listoption_inv {A B} (f : A -> B) (l : list (option A)) :
map f (listoption_inv l) = listoption_inv (map (option_map f) l).