the edges of this path \df{edges covered by~$e$}.
\:An edge~$e$ is called \df{light with respect to~$T$} (or just \df{$T$-light}) if it covers a heavier edge, i.e., if there
is an edge $f\in T[e]$ such that $w(f) > w(e)$.
-\:An edge~$e$ is called \df{$T$-heavy} if it is not $T$-light.
+\:An edge~$e$ is called \df{$T$-heavy} if it covers a~lighter edge.
\endlist
\rem
-Please note that the above properties also apply to tree edges
-which by definition cover only themselves and therefore they are always heavy.
+Edges of the tree~$T$ itself are neither heavy nor light. We will sometimes
+use the name \df{non-heavy} for edges which are either light or contained
+in the tree.
\lemman{Light edges}\id{lightlemma}%
Let $T$ be a spanning tree. If there exists a $T$-light edge, then~$T$