reserve n, m for Element of NAT;
reserve z for Complex;

theorem Th1:
  for f be PartFunc of COMPLEX,COMPLEX st f is total holds dom (Re
  f) = COMPLEX & dom (Im f) = COMPLEX
proof
  let f be PartFunc of COMPLEX,COMPLEX;
  assume f is total;
  then dom f = COMPLEX by PARTFUN1:def 2;
  hence thesis by COMSEQ_3:def 3,def 4;
end;
