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

theorem Th55:
  z-(z1-z2)=z-z1+z2
proof
 -(z1-z2)=(-1q)*(z1-z2) by QUATERN2:19
    .=(-1q)*z1-(-1q)*z2 by QUATERN2:24;
then z-(z1-z2)= z+((-1q)*z1-(-z2)) by QUATERN2:19
    .=z+(-1q)*z1+z2 by QUATERN2:2;
  hence thesis by QUATERN2:19;
end;
