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 Th34:
  <:{},X,Y:> = {}
proof
  dom {} c= X & rng {} c= Y;
  hence thesis by Th31;
end;
