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 Th113:
  for n being odd Element of NAT st n <= len W holds W.find(W.n)
  <= n & W.rfind(W.n) >= n
proof
  let n be odd Element of NAT;
  assume
A1: n <= len W;
  then
A2: W.n in W.vertices() by Lm45;
  hence W.find(W.n) <= n by A1,Def19;
  thus thesis by A1,A2,Def21;
end;
