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

theorem
  <j>^3=-<j>
proof
 <j>*<j>*<j> = ([* 0*0-0*0-1*1-0*0, 0*0+0*0+0*0-0*1, 0*1+0*1+0*0-0*0, 0*0
  +0*0+0*1-1*0 *])* [*0,0,jj,0*] by QUATERNI:def 10
    .= [* (-1)*0-0*0-0*1-0*0,(-1)*0+0*0+0*0-0*1, (-1)*1+0*0+0*0-0*0, (-1)*0+
  0*0+0*1-0*0 *] by QUATERNI:def 10
    .=-[*0,0,jj,0*] by QUATERN2:4;
  hence thesis;
end;
