reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:51
  X (/\) {x} = {x} implies x in X
proof
  assume
A1: X (/\) {x} = {x};
  let i;
  assume
A2: i in I;
  then X.i /\ {x.i} = X.i /\ {x}.i by Def1
    .= (X (/\) {x}).i by A2,PBOOLE:def 5
    .= {x.i} by A1,A2,Def1;
  hence thesis by ZFMISC_1:45;
end;
