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 n being odd Element of NAT st n <= len W holds W.vertexAt(n) = W
  .vertexSeq().((n+1) div 2)
proof
  let n be odd Element of NAT;
  set m = (n+1) div 2;
  assume
A1: n <= len W;
  then
A2: 2 * m - 1 = n by Th66;
A3: m <= len W.vertexSeq() by A1,Th66;
A4: 1 <= m by A1,Th66;
  W.vertexAt(n) = W.n by A1,Def8;
  hence thesis by A2,A4,A3,Def14;
end;
