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

theorem Th19:
  for G2, E for G1 being reverseEdgeDirections of G2, E, v1, v2 being object
  holds (ex W1 being Walk of G1 st W1 is_Walk_from v1,v2) iff
    (ex W2 being Walk of G2 st W2 is_Walk_from v1,v2)
proof
  let G2, E;
  let G1 be reverseEdgeDirections of G2, E;
  let v1, v2 be object;
  hereby
    given W1 being Walk of G1 such that
      A1: W1 is_Walk_from v1,v2;
    reconsider W2=W1 as Walk of G2 by Th15;
    take W2;
    thus W2 is_Walk_from v1,v2 by A1, GLIB_001:19;
  end;
  given W2 being Walk of G2 such that
    A2: W2 is_Walk_from v1,v2;
  reconsider W1=W2 as Walk of G1 by Th14;
  take W1;
  thus thesis by A2, GLIB_001:19;
end;
