reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  <:{},X,Y:> is total implies X = {}
 proof
   dom {} = {};
  hence thesis by Th40,XBOOLE_1:3;
 end;
