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
  e in W.edges() implies ex v1, v2 being Vertex of G, n being odd
  Element of NAT st n+2 <= len W & v1 = W.n & e = W.(n+1) & v2 = W.(n+2) & e
  Joins v1, v2,G by Lm47;
