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
  W is Trail-like iff for m,n being even Element of NAT st 1 <= m & m <
  n & n <= len W holds W.m <> W.n by Lm57;
