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 :: CLOSURE:12
  id (Bool A) is monotonic SetOp of A
proof
  reconsider f = id (Bool A) as SetOp of A;
  f is monotonic;
  hence thesis;
end;
