
theorem Th1:
  for A be non empty set for L be lower-bounded LATTICE for d be
  distance_function of A,L holds succ {} c= DistEsti(d)
proof
  let A be non empty set;
  let L be lower-bounded LATTICE;
  let d be distance_function of A,L;
  succ {} c= DistEsti(d) or DistEsti(d) in succ {} by ORDINAL1:16;
  then succ {} c= DistEsti(d) or DistEsti(d) c= {} by ORDINAL1:22;
  hence thesis by LATTICE5:20,XBOOLE_1:3;
end;
