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 W holds len W
.cut(m,n) + m = n+1 & for i being Element of NAT st i < len W.cut(m,n) holds W
  .cut(m,n).(i+1) = W.(m+i) & m+i in dom W by Lm15;
