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 P being Subset of TOP-REAL 2, f being non constant standard
  special_circular_sequence st P is_a_component_of (L~f)` holds P = RightComp f
  or P = LeftComp f
proof
  let P be Subset of TOP-REAL 2, f be non constant standard
  special_circular_sequence;
  assume P is_a_component_of (L~f)`;
  then ex B1 being Subset of (TOP-REAL 2)|(L~f)` st B1 = P & B1
  is a_component by CONNSP_1:def 6;
  hence thesis by GOBRD14:12;
end;
