
theorem Th27:
  for G1, G2 being _Graph, W1 being Walk of G1, W2 being Walk of G2
  st W1 = W2 holds W1 is Path-like implies W2 is Path-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 Path-like;
  then W2 is Trail-like & for m, n being odd Element of NAT
    st m < n & n <= len W2 holds W2.m = W2.n implies m = 1 & n = len W2
    by A1, Th26, GLIB_001:def 28;
  hence W2 is Path-like by GLIB_001:def 28;
end;
