reserve i,j,k,n for Nat,
  D for non empty set,
  f, g for FinSequence of D;
reserve G for Go-board,
  f, g for FinSequence of TOP-REAL 2,
  p for Point of TOP-REAL 2,
  r, s for Real,
  x for set;

theorem Th8:
  f is_sequence_on G implies
 for k being Nat st 1 <= k & k+1 <= len f
  holds f/.k in left_cell(f,k,G) & f/.k in right_cell(f,k,G)
proof
  assume that
A1: f is_sequence_on G;
  let k be Nat such that
A2: 1 <= k & k+1 <= len f;
  set p = f/.k;
  LSeg(f,k) = LSeg(f/.k, f/.(k+1)) by A2,TOPREAL1:def 3;
  then p in LSeg(f,k) by RLTOPSP1:68;
  then p in left_cell(f,k,G) /\ right_cell(f,k,G) by A1,A2,GOBRD13:29;
  hence thesis by XBOOLE_0:def 4;
end;
