
theorem Th58:
  for G1 being _Graph, G2 being Subgraph of G1,
    W1 being Walk of G1, W2 being Walk of G2 st W1 = W2
  holds W1 is Cycle-like iff W2 is Cycle-like
proof
  let G1 be _Graph, G2 be Subgraph of G1;
  let W1 be Walk of G1, W2 be Walk of G2;
  assume A1: W1 = W2;
  hereby
    assume W1 is Cycle-like;
    then W2 is closed & W2 is Path-like & W2 is non trivial
      by A1, GLIB_001:176;
    hence W2 is Cycle-like;
  end;
  assume W2 is Cycle-like;
  then W1 is closed & W1 is Path-like & W1 is non trivial by A1, GLIB_001:176;
  hence W1 is Cycle-like;
end;
