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_1:50
  I is non empty implies {x,y} (\/) X <> EmptyMS I
proof
  assume that
A1: I is non empty and
A2: {x,y} (\/) X = EmptyMS I;
  consider i being object such that
A3: i in I by A1,XBOOLE_0:def 1;
  {x.i,y.i} \/ X.i <> {};
  then {x,y}.i \/ X.i <> {} by A3,Def2;
  then ({x,y} (\/) X).i <> {} by A3,PBOOLE:def 4;
  hence contradiction by A2,PBOOLE:5;
end;
