
theorem Th9:
  for a,b be Element of F_Complex holds Re (a - b) = Re a - Re b &
  Im (a - b) = Im a - Im b
proof
  let a,b be Element of F_Complex;
  reconsider x = a, y =b as Element of COMPLEX by COMPLFLD:def 1;
  thus Re (a-b) = Re (x-y) by COMPLFLD:3
    .= Re a - Re b by COMPLEX1:19;
  thus Im (a-b) = Im (x-y) by COMPLFLD:3
    .= Im a - Im b by COMPLEX1:19;
end;
