for k being Nat
for G being Go-board
for f, g being FinSequence of (TOP-REAL 2) st f is_sequence_on G & f is special & L~ g c= L~ f & 1 <= k & k + 1 <= len f holds
for A being Subset of (TOP-REAL 2) st ( A = (right_cell (f,k,G)) \ (L~ g) or A = (left_cell (f,k,G)) \ (L~ g) ) holds
A is connected