reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem
  X c= Y (\) X implies X = EmptyMS I
proof
  assume
A1: X c= Y (\) X;
    let i be object;
    assume
A2: i in I;
    then X.i c= (Y (\) X).i by A1;
    then X.i c= Y.i \ X.i by A2,Def6;
    hence X.i = {} by XBOOLE_1:38
      .= EmptyMS I.i;
end;
