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

theorem Th54:
  z-(z1+z2)=z-z1-z2
proof
A1: z-z1-z2=z+(-1q)*z1+(-z2) by QUATERN2:19
    .=z+(-1q)*z1+(-1q)*z2 by QUATERN2:19;
 -(z1+z2)=(-1q)*(z1+z2) by QUATERN2:19
    .=(-1q)*z1+(-1q)*z2 by QUATERN2:17;
  hence thesis by A1,QUATERN2:2;
end;
