Definition Cobham_to_BC n e :=
  comp n 0 (Cobham_to_BC'' n e) 
  (map (proj n 0) (seq 0 n))
  (map (proj n 0) (seq 0 n)).

Lemma Cobham_to_BC_inf : forall e n, arity e = ok_arity n -> arities (Cobham_to_BC n e) = ok_arities n 0.