(* Require Import Vector. *)
(* Definition vector X Y := Vector.t Y (|elem X|). *)
Definition finfunc_table (A : finType) (B: Type) (f: A -> B) :=
List.map (fun x => (x, f x)) (elem A).
(* Now we prove that the tranformation of a function of finite domain to a table is correct *)

Lemma finfunc_sound (A : finType) (B : Type) (f: A -> B) a b: (a,b) el finfunc_table f -> b = f a.