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 n in dom W & n+1 in
  dom W & n+2 in dom W
proof
  let n be odd Element of NAT;
A1: 1 <= n by ABIAN:12;
A2: 1 <= n+1 by NAT_1:12;
A3: 1 <= n+2 by NAT_1:12;
  assume
A4: n < len W;
  then
A5: n+1 <= len W by NAT_1:13;
  n+2 <= len W by A4,Th1;
  hence thesis by A4,A1,A2,A3,A5,FINSEQ_3:25;
end;
