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 being object holds
  e Joins W.last(),x,G implies W.addEdge(e).(len W + 1) = e & W.addEdge(
e).(len W + 2) = x & for n being Element of NAT st n in dom W holds W.addEdge(e
  ).n = W.n by Lm38;
