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

theorem
  (z1+z2-z3)*z4=z1*z4+z2*z4-z3*z4
proof
 (z1+z2-z3)*z4=(z1+z2)*z4-z3*z4 by QUATERN2:23
    .=z1*z4+z2*z4-z3*z4 by QUATERN2:18;
  hence thesis;
end;
