reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;

theorem Th80:
  for G2, G1 for W2 being Walk of G2, W1 being Walk of G1 st W1 = W2 holds
    (W1 is closed iff W2 is closed) &
    (W1 is directed iff W2 is directed) &
    (W1 is trivial iff W2 is trivial) &
    (W1 is Trail-like iff W2 is Trail-like) &
    (W1 is Path-like iff W2 is Path-like) &
    (W1 is vertex-distinct iff W2 is vertex-distinct) &
    (W1 is Cycle-like iff W2 is Cycle-like)
proof
  let G2, G1;
  A1: G2 is Subgraph of G1 by Th61;
  let W2 being Walk of G2;
  let W1 being Walk of G1;
  assume W1 = W2;
  hence thesis by A1, Th58, GLIB_001:176;
end;
