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
  E (\) A in Bool M
proof
  E c= M by PBOOLE:def 18;
  then E (\) A c= M by MBOOLEAN:15;
  then E (\) A is ManySortedSubset of M by PBOOLE:def 18;
  hence thesis by Def1;
end;
