reserve z1,z2,z3,z4,z for Quaternion;

theorem
  -(z1-z2+z3)=-z1+z2-z3
proof
 -(z1-z2+z3)=-(z1-z2)-z3 by Th52
    .=-z1+z2-z3 by Th53;
  hence thesis;
end;
