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 (\+\) T in Bool M
proof
  T c= M by PBOOLE:def 18;
  then
A1: T (\) E c= M by MBOOLEAN:15;
  E c= M by PBOOLE:def 18;
  then E (\) T c= M by MBOOLEAN:15;
  then E (\+\) T c= M by A1,PBOOLE:91;
  then E (\+\) T is ManySortedSubset of M by PBOOLE:def 18;
  hence thesis by Def1;
end;
