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

theorem
  <i>"=-<i>
proof
A1: Im3 <i>"= - (Im3 <i>) / (|.<i>.|^2) by QUATERN2:29
    .= 0 by QUATERNI:30;
A2: Im2 <i>" = -(Im2 <i>) / (|.<i>.|^2) by QUATERN2:29
    .= 0 by QUATERNI:30;
A3: Im1 <i>" = -(Im1 <i>) / (|.<i>.|^2) by QUATERN2:29
    .= -1 by QUATERNI:30;
  Rea <i>" = (Rea <i>) / (|.<i>.|^2) by QUATERN2:29
    .= 0 by QUATERNI:30;
  then <i>"=[*-0,-1,-0,-0*] by A3,A2,A1,QUATERNI:24
    .=-[*0,jj,0,0*] by QUATERN2:4
    .=-<i> by Lm2,QUATERNI:def 6;
  hence thesis;
end;
