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

theorem
  X (\) Y = X implies X misses Y
proof
  assume
A1: X (\) Y = X;
  let i be object;
  assume i in I;
  then X.i \ Y.i = X.i by A1,Def6;
  hence thesis by XBOOLE_1:83;
end;
