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
  W1.last() = W2.first() implies for n being Element of NAT st n < len
W2 holds W1.append(W2).(len W1 + n) = W2.(n+1) & (len W1 + n) in dom W1.append(
  W2) by Lm13;
