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
 for e,x,y,z being object holds
  W is_Walk_from x,y & e Joins y,z,G implies W.addEdge(e) is_Walk_from x
  ,z by Lm39;
