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 & W is_Walk_from x,y & e DJoins y,z,G implies W.addEdge(
  e) is directed & W.addEdge(e) is_Walk_from x,z by Lm52;
