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 n being even Element of NAT st n in dom W holds ex naa1 being odd
Element of NAT st naa1 = n-1 & n-1 in dom W & n+1 in dom W & W.n Joins W.(naa1)
  , W.(n+1),G by Lm2;
