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

theorem
  |.z1*z2*z3.| ^2 = |.z1.| ^2 * |.z2.| ^2 * |.z3.| ^2
proof
  |.z1*z2*z3.| ^2 = |.z1*(z2*z3).| ^2 by QUATERN2:16
    .= |.z1.| ^2 * |.z2*z3.| ^2 by Th17
    .= |.z1.| ^2 * (|.z2.| ^2 * |.z3.| ^2) by Th17
    .= |.z1.| ^2 * |.z2.| ^2 * |.z3.| ^2;
  hence thesis;
end;
