reserve i,j,x,y for object,
  f,g for Function;

theorem Th2:
  for I being non empty set, B being non-empty ManySortedSet of I
  holds union rng B is non empty
proof
  let I be non empty set, B be non-empty ManySortedSet of I;
  set i = the Element of I;
  i in I;
  then i in dom B by PARTFUN1:def 2;
  then B.i in rng B by FUNCT_1:def 3;
  hence thesis by ORDERS_1:6;
end;
