reserve G,G1,G2 for _Graph;
reserve W,W1,W2 for Walk of G;
reserve e,x,y,z for set;
reserve v for Vertex of G;
reserve n,m for Element of NAT;

theorem
  W is directed iff for n being odd Element of NAT st n < len W holds W.
  (n+1) DJoins W.n, W.(n+2), G by Lm51;
