theorem
  |.z*z.| = (Rea z)^2 + (Im1 z)^2 + (Im2 z)^2 + (Im3 z)^2
proof
A1: (Rea z)^2 + (Im1 z)^2 + (Im2 z)^2 + (Im3 z)^2 >= 0 by Th67;
  |.z.| * |.z.| =(sqrt ((Rea z)^2 + (Im1 z)^2 + (Im2 z)^2 + (Im3 z)^2))^2
    .= (Rea z)^2 + (Im1 z)^2 + (Im2 z)^2 + (Im3 z)^2 by A1,SQUARE_1:def 2;
  hence thesis by Th80;
end;
