theorem Th53:
  -(z1-z2)=-z1+z2
proof
 -(z1-z2)=(-1q)*(z1-z2) by QUATERN2:19
    .=(-1q)*z1-(-1q)*z2 by QUATERN2:24
    .=(-1q)*z1-(-z2) by QUATERN2:19;
  hence thesis by QUATERN2:19;
end;
