  We automatically verify the crucial steps in the original proof of
correctness of an algorithm which, given a geometric graph satisfying certain
additional properties removes edges in a systematic way for producing a
connected graph in which edges do not (geometrically) intersect. The challenge
in this case is representing and reasoning about geometric properties of graphs
in the Euclidean plane, about their vertices and edges, and about connectivity.
For modelling the geometric aspects, we use an axiomatization of plane
geometry; for representing the graph structure we use additional predicates;
for representing certain classes of paths in geometric graphs we use linked
lists.
