theorem Th174: :: GLIB_001:176

for G1 being _Graph
for G2 being Subgraph of G1
for W1 being Walk of G1
for W2 being Walk of G2 st W1 = W2 holds
( ( W1 is closed implies W2 is closed ) & ( W2 is closed implies W1 is closed ) & ( W1 is directed implies W2 is directed ) & ( W2 is directed implies W1 is directed ) & ( W1 is trivial implies W2 is trivial ) & ( W2 is trivial implies W1 is trivial ) & ( W1 is Trail-like implies W2 is Trail-like ) & ( W2 is Trail-like implies W1 is Trail-like ) & ( W1 is Path-like implies W2 is Path-like ) & ( W2 is Path-like implies W1 is Path-like ) & ( W1 is vertex-distinct implies W2 is vertex-distinct ) & ( W2 is vertex-distinct implies W1 is vertex-distinct ) )