(* 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_cor (A : finType) (B:Type) (f: A -> B) a b b' : (a,b) el finfunc_table f -> (a,b') el finfunc_table f -> b = b'.