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 len W1 <= len W1.append(W2) &
  len W2 <= len W1.append(W2) by Lm10;
