reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem Th2:
  for f being Function st rng f c= Y holds f is Function of dom f, Y
proof
  let f be Function;
  assume rng f c= Y;
  then reconsider R = f as Relation of dom f,Y by RELSET_1:4;
  Y = {} or Y <> {};
  then R is quasi_total by Def1;
  hence thesis;
end;
