let G1, G2 be _Graph; :: thesis: for W1 being Walk of G1
for W2 being Walk of G2 st W1 = W2 & W1 is Cycle-like holds
W2 is Cycle-like
let W1 be Walk of G1; :: thesis: for W2 being Walk of G2 st W1 = W2 & W1 is Cycle-like holds
W2 is Cycle-like
let W2 be Walk of G2; :: thesis: ( W1 = W2 & W1 is Cycle-like implies W2 is Cycle-like )
assume A1: W1 = W2 ; :: thesis: ( not W1 is Cycle-like or W2 is Cycle-like )
assume W1 is Cycle-like ; :: thesis: W2 is Cycle-like
then ( W2 is closed & W2 is Path-like & W2 is trivial ) by A1, Th27, GLIB_001:121;
hence W2 is Cycle-like ; :: thesis: verum