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 Th12:
  B1 in A implies A \ B1 is closed unbounded
proof
  assume
A1: B1 in A;
  [#] A is closed unbounded by Th10;
  hence thesis by A1,Th11;
end;
