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 Th9:
  for n being odd Element of NAT st n < len W holds
  W.(n+1) in W.vertexAt(n).edgesInOut()
proof
  let n be odd Element of NAT;
  assume
A1: n < len W;
  then
A2: W.vertexAt(n) = W.n by Def8;
  W.(n+1) Joins W.n, W.(n+2), G by A1,Def3;
  hence thesis by A2,GLIB_000:62;
end;
