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)).

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.