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 x,y being object holds
  for W1 being Walk of G1, W2 being Walk of G2 st W1 = W2 holds W1
  is_Walk_from x,y iff W2 is_Walk_from x,y;
