Then $K$ appears in the last position in the list.
The vector $v$ has at least $n$ ones in its last $m$ positions.
This is the same as asking which row vectors in $R$ have differing entries at positions $i$ and $j$.
We are now in a position to prove our main result. [ Better: We can now prove]
This puts us in a position to apply Lemma 2 to deduce that ......
After receiving his PhD he took a position at the University of Texas.