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

theorem
  for G2 for G1 being reverseEdgeDirections of G2
  for W2 being Walk of G2, W1 being Walk of G1 st W1 = W2
  holds (W1 is directed iff W2.reverse() is directed)
proof
  let G2;
  let G1 be reverseEdgeDirections of G2;
  let W2 be Walk of G2, W1 be Walk of G1;
  assume A1: W1 = W2;
  W2.edges() c= the_Edges_of G2;
  hence thesis by A1, Th16;
end;
