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 Th13:
  for X,Y being Subset of A holds (X is stationary & X c= Y
  implies Y is stationary)
proof
  let X,Y be Subset of A;
  assume
A1: X is stationary;
  assume
A2: X c= Y;
  let Z1 be Subset of A;
  assume Z1 is closed unbounded;
  then X /\ Z1 is non empty by A1;
  then
A3: ex x being object st x in X /\ Z1 by XBOOLE_0:def 1;
  X /\ Z1 c= Y /\ Z1 by A2,XBOOLE_1:26;
  hence thesis by A3;
end;
