reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem
  for f being Function of X,D holds (.:f)"B c= bool X
proof
  let f be Function of X,D;
  dom f = X by FUNCT_2:def 1;
  hence thesis by Th11;
end;
