theorem :: GLIB_001:55

for G being _Graph
for W being Walk of G
for m, n being odd Element of NAT st m <= n & n <= len W & W . m = W . n holds
for x being Element of NAT st m <= x & x <= len (W .remove (m,n)) holds
( (W .remove (m,n)) . x = W . ((x - m) + n) & (x - m) + n is Element of NAT & (x - m) + n <= len W ) by Lm30;