# How to prove substring is a partial order

u is defined to be a substring of a string v if v = xuy for some string x and y. Either or both possibly empty.

How to you prove that a substring relation on any set of strings is a partial order?

• What have you tried? Where did you get stuck? Try using the definition of a partial order. – Yuval Filmus Oct 1 '13 at 4:35
• Do you know the proof for the subsets of a set $A$ ordered by $\subseteq$? If you do, what is different when you consider substrings? – frafl Oct 1 '13 at 7:18

Hint: show that if $u$ is a substring of $v$ and $v$ is a substring of $w$ then $u$ is a substring of $w$.