On 16 Mrz., 12:26, William Hughes <wpihug...@gmail.com> wrote: > On Mar 16, 10:30 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 15 Mrz., 23:27, William Hughes <wpihug...@gmail.com> wrote: > > > > On Mar 15, 8:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > Let's first prove that already two cannot be necessary by the fact > > > > that two always can be replaced by one of them without changing the > > > > contents. > > > > This is true but the fact that the two lines are > > > necessary has nothing to do with their contents. Two lines > > > cannot be replaced by one of them without changing the number > > > of lines. > > > Why should line-numbers be changed? Perhaps we are misunderstanding > > each other. > > I said "number of lines" not "line-numbers". > If you replace two lines by one of them, you do > not change the contents, but you do change the number > of lines. Since the number of lines is important > and the contents are not, you cannot replace > two lines with one line.
Ok, I understand. Anyhow, if the number of lines is not empty, then there must remain at least one line as a necessary line. That line has a line-number in the original list. I think that if one more more lines are necessary, as you claim, then there must be a set of line- numbers which is not empty and, therefore, has a least element.