for G being _Graph
for W1, W2 being Walk of G st W1 .last() = W2 .first() holds
for n being Element of NAT st n < len W2 holds
( (W1 .append W2) . ((len W1) + n) = W2 . (n + 1) & (len W1) + n in dom (W1 .append W2) ) by Lm13;