reserve z,z1,z2,z3,z4 for Element of F_Complex;

theorem
  (z1 - z2)*' = z1*' - z2*'
proof
  reconsider z19=z1,z29=z2 as Element of COMPLEX by Def1;
  z19 - z29 = z1 - z2 by Th3;
  hence (z1 - z2)*' = z19*' - z29*' by COMPLEX1:34
    .= z1*' - z2*' by Th3;
end;
