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 Th7:
  X is unbounded implies X is non empty
proof
  set B1 = the Element of A;
  assume X is unbounded;
  then ex C st C in X & B1 c= C by Th6;
  hence thesis;
end;
