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
  W is closed iff W.reverse() is closed
proof
  W is closed iff W.reverse().last() = W.last() by Th21;
  then W is closed iff W.reverse().last() = W.reverse().first() by Th21;
  hence thesis;
end;
