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;
reserve g, h for SetOp of M;

theorem :: CLOSURE:17
  (g is reflexive & for X being Element of Bool M holds g.X c= X)
  implies g is idempotent
proof
  assume that
A1: g is reflexive and
A2: for X being Element of Bool M holds g.X c= X;
  let X be Element of Bool M;
A3: g.X c= g.(g.X) by A1;
   g.(g.X) c= g.X by A2;
  hence thesis by A3,PBOOLE:146;
end;
