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

theorem Th14:
  for G2, E for G1 being reverseEdgeDirections of G2, E, W2 being Walk of G2
  holds W2 is Walk of G1
proof
  let G2, E;
  let G1 be reverseEdgeDirections of G2, E;
  let W2 be Walk of G2;
  per cases;
  suppose E c= the_Edges_of G2;
    W2 is FinSequence of the_Vertices_of G1 \/ the_Edges_of G2 by Th4;
    then A1: W2 is FinSequence of the_Vertices_of G1 \/ the_Edges_of G1
      by Th4;
    W2.1 in the_Vertices_of G2 by GLIB_001:def 3;
    then A2: W2.1 in the_Vertices_of G1 by Th4;
    for n being odd Element of NAT st n < len W2 holds
      W2.(n+1) Joins W2.n, W2.(n+2), G1 by Th9, GLIB_001:def 3;
    hence thesis by A1, A2, GLIB_001:def 3;
  end;
  suppose not (E c= the_Edges_of G2);
    then G1 == G2 by Def1;
    hence thesis by GLIB_001:179;
  end;
end;
