reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem
  for f being non constant standard special_circular_sequence st f
is_sequence_on G for k st 1 <= k & k+1 <= len f holds Int right_cell(f,k,G) c=
  RightComp f & Int left_cell(f,k,G) c= LeftComp f
proof
  let f be non constant standard special_circular_sequence such that
A1: f is_sequence_on G;
  let k such that
A2: 1 <= k & k+1 <= len f;
  Int right_cell(f,k,G) misses L~f by A1,A2,JORDAN9:15;
  then
A3: Int right_cell(f,k,G) c= right_cell(f,k,G)\L~f by TOPS_1:16,XBOOLE_1:86;
  Int left_cell(f,k,G) misses L~f by A1,A2,JORDAN9:15;
  then
A4: Int left_cell(f,k,G) c= left_cell(f,k,G)\L~f by TOPS_1:16,XBOOLE_1:86;
  right_cell(f,k,G)\L~f c= RightComp f by A1,A2,JORDAN9:27;
  hence Int right_cell(f,k,G) c= RightComp f by A3;
  left_cell(f,k,G)\L~f c= LeftComp f by A1,A2,JORDAN9:27;
  hence thesis by A4;
end;
