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 m,n being odd Element of NAT st m <= n & n <= len W1 & W1.last() =
  W2.first() holds W1.append(W2).cut(m,n) = W1.cut(m,n) by Lm21;
