Definition poly_BC (p : pol) : BC :=
  plusl_e (fst p) (map (poly_BC_mon (fst p)) (snd p)).

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.