Let G $=($V$,$E$)$ be a directed graph. After algorithm DFS$($G$)$ has terminated,

each vertex has a pre$-$ and post$-$number. Let u and v be two distinct vertices in V $.$ Assume

that both of the following are true:

$$ There is a directed path in G from u to v$.$

$$ pre$($u$)<$ pre$($v$).$

Professor Lionel Messi claims that, in the DFS$-$forest, v must be in the subtree of u$.$

Is Professor Messi$$s claim correct? As always, justify your answer.