
theorem
  for G1, G2 being _Graph, W1 being Walk of G1, W2 being Walk of G2
  st W1 = W2 holds W1 is Cycle-like implies W2 is Cycle-like
proof
  let G1, G2 be _Graph;
  let W1 be Walk of G1, W2 be Walk of G2;
  assume A1: W1 = W2;
  assume W1 is Cycle-like;
  then W2 is closed Path-like non trivial
    by A1, Th27, GLIB_001:121;
  hence thesis;
end;
