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 Th21:
  A in SF implies A in' |:SF:|
proof
  assume
A1: A in SF;
  let i be object;
  assume i in I;
  then |:SF:|.i = { x.i where x is Element of Bool M : x in SF } by A1,Th14;
  hence thesis by A1;
end;
