reserve A,B for limit_ordinal infinite Ordinal;
reserve B1,B2,B3,B5,B6,D, C for Ordinal;
reserve X for set;
reserve X for Subset of A;

theorem
  X c= B1 implies limpoints X c= succ B1
proof
A1: X /\ A = X by XBOOLE_1:28;
  assume X c= B1;
  then A /\ limpoints X c= succ B1 by A1,Th16;
  hence thesis by XBOOLE_1:28;
end;
