theorem
  for f being homogeneous to-naturals NAT*-defined Function holds
  arity <*f*> = arity f
proof
  let f be homogeneous to-naturals NAT*-defined Function;
  rng <*f*> = {f} by FINSEQ_1:38;
  then f in rng <*f*> by TARSKI:def 1;
  hence thesis by Def4;
end;
