(*For compability:  A more cbn-friendly version of Vector.to_list *)
(* TODO: rework such that every lemma is in terms of Vector.to_list and we can use vector_to_list_correct to transfer? *)
Fixpoint vector_to_list (X : Type) (n : nat) (v : Vector.t X n) : list X :=
match v with
| Vector.nil _ => List.nil
| Vector.cons _ x n v' => x :: vector_to_list v'
end.

Lemma vector_to_list_map (X Y : Type) (f : X -> Y) (n : nat) (v : Vector.t X n) :
map f (vector_to_list v) = vector_to_list (Vector.map f v).