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

theorem
  <j>"=-<j>
proof
A1: Im3 <j>"= - (Im3 <j>) / (|.<j>.|^2) by QUATERN2:29
    .= 0 by QUATERNI:31;
A2: Im2 <j>" = -(Im2 <j>) / (|.<j>.|^2) by QUATERN2:29
    .= -1 by QUATERNI:31;
A3: Im1 <j>" = -(Im1 <j>) / (|.<j>.|^2) by QUATERN2:29
    .= 0 by QUATERNI:31;
  Rea <j>" = (Rea <j>) / (|.<j>.|^2) by QUATERN2:29
    .= 0 by QUATERNI:31;
  then <j>"=[*-0,-0,-jj,-0*] by A3,A2,A1,QUATERNI:24
    .=-<j> by QUATERN2:4;
  hence thesis;
end;
