theorem :: GOBOARD8:9
for f being non constant standard special_circular_sequence
for k being Nat st 1 <= k & k + 2 <= len f holds
for i being Nat st 1 <= i & i + 2 <= len (GoB f) & f /. (k + 1) = (GoB f) * ((i + 1),(width (GoB f))) & ( ( f /. k = (GoB f) * ((i + 2),(width (GoB f))) & f /. (k + 2) = (GoB f) * ((i + 1),((width (GoB f)) -' 1)) ) or ( f /. (k + 2) = (GoB f) * ((i + 2),(width (GoB f))) & f /. k = (GoB f) * ((i + 1),((width (GoB f)) -' 1)) ) ) holds
LSeg (((1 / 2) * (((GoB f) * (i,((width (GoB f)) -' 1))) + ((GoB f) * ((i + 1),(width (GoB f)))))),(((1 / 2) * (((GoB f) * (i,(width (GoB f)))) + ((GoB f) * ((i + 1),(width (GoB f)))))) + |[0,1]|)) misses L~ f