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

theorem
  z1 = z1 + z - z
proof
  reconsider z19=z1,z9=z as Element of COMPLEX by Def1;
  thus z1 + z - z = z19 + z9 - z9 by Th3
    .= z1;
end;
