End Positions.
Notation nthe n A := (nth_error A n).

Lemma pos_length X d (x : X) l n : pos d x l = Some n -> n < | l |.
Fixpoint omap X Y (f : X -> option Y) l :=
match l with
| nil => nil
| x :: l => match f x with Some y => y :: omap f l | None => omap f l end
end.