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 & W.m = W.n
  holds for x being Element of NAT st m <= x & x <= len W.remove(m,n) holds W
.remove(m,n).x = W.(x - m + n) & x - m + n is Element of NAT & x - m + n <= len
  W by Lm30;
