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

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