
theorem Th26:
  for G1, G2 being _Graph, W1 being Walk of G1, W2 being Walk of G2
  st W1 = W2 holds W1 is Trail-like implies W2 is Trail-like
proof
  let G1, G2 be _Graph;
  let W1 be Walk of G1, W2 be Walk of G2;
  assume W1 = W2;
  then A2: W1.edgeSeq() = W2.edgeSeq() by GLIB_001:86;
  assume W1 is Trail-like;
  then W2.edgeSeq() is one-to-one by A2, GLIB_001:def 27;
  hence W2 is Trail-like by GLIB_001:def 27;
end;
