Definition Cobham_to_BC'' n e :=
comp n n (Cobham_to_BC' n e) [poly_BC (rec_simulation n e)]
(map (proj n n) (seq n n)).

(* Specifications: *)
Lemma Cobham_to_BC''_inf : forall e n,
arity e = ok_arity n ->
arities (Cobham_to_BC'' n e) = ok_arities n n.
Lemma seq_map : forall A len start (f : nat -> A),
map (fun x => f x) (seq start len) = map (fun x => f (x + start)) (seq 0 len).
Lemma Cobham_to_BC''_correct : forall e xl n,
rec_bounded e ->
arity e = ok_arity n ->
length xl = n ->
Sem e xl = sem (Cobham_to_BC'' n e) xl xl.