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

theorem Th18:
  for G2, E for G1 being reverseEdgeDirections of G2, E
  for W2 being Walk of G2, W1 being Walk of G1 st W1 = W2
  holds (W1 is chordal iff W2 is chordal)
proof
  let G2, E;
  let G1 be reverseEdgeDirections of G2, E;
  let W2 be Walk of G2, W1 be Walk of G1;
  assume A1: W1 = W2;
  hence W1 is chordal implies W2 is chordal by Lm4;
  assume A2: W2 is chordal;
  reconsider G3 = G2 as reverseEdgeDirections of G1, E by Th3;
  reconsider W3 = W2 as Walk of G3;
  W3 is chordal by A2;
  hence W1 is chordal by A1, Lm4;
end;
