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

theorem
  |.z1*z2*z3.| = |.z1.|*|.z2.|*|.z3.|
proof
  |.z1*z2*z3.| =|.z1*(z2*z3).| by QUATERN2:16
    .=|.z1.|*|.z2*z3.| by QUATERNI:87
    .=|.z1.|*(|.z2.|*|.z3.|) by QUATERNI:87
    .=|.z1.|*|.z2.|*|.z3.|;
  hence thesis;
end;
