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
  G.walkOf(v).vertexSeq() = <*v*>
proof
  set VS = G.walkOf(v).vertexSeq();
  len G.walkOf(v) + 1 = 2 * len VS by Def14;
  then
A1: 1 + 1 = 2 * len VS by Th12;
  then VS.1 = G.walkOf(v).(2*1-1) by Def14
    .= v;
  hence thesis by A1,FINSEQ_1:40;
end;
