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@@ -216,7 +216,7 @@ One can see that in this process we do not care the actual base $B_{F^*}$ and on
 \autoref{conj:dist} is true when $M$ is a 2D rigidity matroid.
 \end{conjecture}
 
-Try to minic Thorup's proof for graphic matroids. As \autoref{lem:partition} states, spans form a partition on $E-F$.
+Try to minic Thorup's proof for graphic matroids. It follows from \autoref{lem:partition} that spans form a partition on $E-F$.
 Note that for graphic matroids the number of spans is $O((r(E)-r(F))^2)$.
 For any spanning tree $T$, the number of spans hitting $T$ is exactly $r(E)-r(F)$ and these spans have a nice structure. If we contract each component in $G[F]$ to a vertex and consider spans a set of parallel edges, then the set of spans hitting $T$ is a tree (with parallel edges) in $G[F]$.
 For rigidity matroids, the number of rigid components in $F$ cannot be bounded by $r(E)-r(F)$.\footnote{Since the 1-thin cover inducing a cocircuit can have any number of rigid components.}