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_1:45
  {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.i by A1,A2,PBOOLE:def 4;
  hence thesis by ZFMISC_1:39;
end;
