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 W1.append(W2).first() = W1.first() & W1
  .append(W2).last() = W2.last() & W1.append(W2) is_Walk_from W1.first(), W2
  .last() by Lm11;
