Suppose that we change line $3$ of DAG$-$SHORTEST$-$PATHS making the procedure read as follows:

$($DAG$-$SHORTEST$-$PATHS$)($G$,$ w$,$ s$)$

topologically sort the vertices of G

INITIALIZE$-$SINGLE$-$SOURCE$)($G$,$ s$)$

$*$for$*$ the first $|$V$|-1$ vertices, taken in topologically sorted order

$*$for$*$ each vertex v in u

RELAX$)($u$,$ v$,$ w$)$

Show that the procedure remains correct.