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 both 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.