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).first() = W.first() & W
  .addEdge(e).last() = x & W.addEdge(e) is_Walk_from W.first(), x by Lm36;
