reserve i, x, I for set,
  A, B, M for ManySortedSet of I,
  f, f1 for Function;
reserve SF, SG for SubsetFamily of M;
reserve E, T for Element of Bool M;

theorem Th9:
  E (/\) T in Bool M
proof
  E c= M & T c= M by PBOOLE:def 18;
  then E (/\) T c= M (/\) M by PBOOLE:21;
  then E (/\) T is ManySortedSubset of M by PBOOLE:def 18;
  hence thesis by Def1;
end;
