> Your proof covers all lines. We have for all lines l > of the list. > > if l and all its predecessors are removed > and no other line is removed, > then the union of all lines is not changed" > > > > > However, there is no information about what will > happen if you try to apply this to two > lines e.g. l along with all its predecessors > and m along with all its predecessors. > > Now it is easy to see what will happen in this > case. Since we can replace l and m with > one of either l or m, we know what will happen > if we remove two lines. > > Since we can replace l,m and p with > one of either l or m or p, we know what will happen > if we remove three lines. > > It is easy to see we know what > will happen if we remove a natural > number of finite lines. > > However, we do not know what will happen > if we remove an infinite number of > finite lines. > If you really want to accept this potential infinite nonsense, then the exact same will happen when you remove an infinite set of lines as when you remove a finite set of lines. Because any particular set of lines will be finite.