  Kelly's lemma is a basic result on graph reconstruction. It states that given
the deck of a graph $G$ on $n$ vertices, and a graph $F$ on fewer than $n$
vertices, we can count the number of subgraphs of $G$ that are isomorphic to
$F$. Moreover, for a given card $G-v$ in the deck, we can count the number of
subgraphs of $G$ that are isomorphic to $F$ and that contain $v$. We consider
the problem of refining the lemma to count rooted subgraphs such that the root
vertex coincides the deleted vertex. We show that such counting is not possible
in general, but a multiset of rooted subgraphs of a fixed height $k$ can be
counted if $G$ has radius more than $k$. We also prove a similar result for the
edge reconstruction problem.
