theorem Th41: :: GLIB_006:37

for G being _Graph
for W1, W2, W3 being Walk of G st W2 is_odd_substring_of W1, 0 & W2 .first() = W3 .first() & W2 .last() = W3 .last() holds
(W1 .replaceWith (W2,W3)) .edges() = (((W1 .cut (1,(W1 .findFirstVertex W2))) .edges()) \/ (W3 .edges())) \/ ((W1 .cut ((W1 .findLastVertex W2),(len W1))) .edges())