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

theorem
  x in X (\) Y implies x in X
proof
  assume
A1: x in X (\) Y;
  thus x in X
  proof
    let i be object;
    assume
A2: i in I;
    then x.i in (X (\) Y).i by A1;
    then x.i in X.i \ Y.i by A2,Def6;
    hence thesis;
  end;
end;
