reserve i, j, n for Nat,
  f for non constant standard special_circular_sequence,
  g for clockwise_oriented non constant standard special_circular_sequence,
  p, q for Point of TOP-REAL 2,
  P for Subset of TOP-REAL 2,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board;

theorem Th17:
  p in LeftComp f iff not p in L~f & not p in RightComp f
proof
  LeftComp f misses RightComp f by Th14;
  then
A1: (L~f)` = LeftComp f \/ RightComp f & LeftComp f /\ RightComp f = {} by
GOBRD12:10;
  p in L~f iff not p in (L~f)` by XBOOLE_0:def 5;
  hence thesis by A1,XBOOLE_0:def 3,def 4;
end;
