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 is stationary implies X is unbounded
proof
  assume
A1: X is stationary;
  assume X is bounded;
  then consider B1 such that
A2: B1 in A and
A3: X c= B1 by Th4;
  (A \ B1) misses B1 by XBOOLE_1:79;
  then (A \ B1) misses X by A3,XBOOLE_1:63;
  then
A4: (A \ B1) /\ X = {} by XBOOLE_0:def 7;
  A \ B1 is closed unbounded by A2,Th12;
  hence contradiction by A1,A4;
end;
