let G1, G2 be _Graph; :: thesis: for W1 being Walk of G1
for W2 being Walk of G2 st W1 = W2 & W1 is closed holds
W2 is closed
let W1 be Walk of G1; :: thesis: for W2 being Walk of G2 st W1 = W2 & W1 is closed holds
W2 is closed
let W2 be Walk of G2; :: thesis: ( W1 = W2 & W1 is closed implies W2 is closed )
assume that
A1: W1 = W2 and
A2: W1 is closed ; :: thesis: W2 is closed
W2 . 1 = W2 . (len W2) by A1, A2, Th119;
hence W2 is closed by Th119; :: thesis: verum