reserve G, G2 for _Graph, V, E for set,
  v for object;

theorem
  for G2, E for G1 being reverseEdgeDirections of G2, E
  for v1 being Vertex of G1, v2 being Vertex of G2 st v1 = v2
  holds (v1 is isolated iff v2 is isolated) &
    (v1 is endvertex iff v2 is endvertex) &
    (v1 is cut-vertex iff v2 is cut-vertex)
proof
  let G2, E;
  let G1 be reverseEdgeDirections of G2, E;
  let v1 be Vertex of G1, v2 be Vertex of G2;
  assume A1: v1 = v2;
  G2 is reverseEdgeDirections of G1, E by Th3;
  hence thesis by A1, Lm5;
end;
