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 holds (Cl
  RightComp(f))` = LeftComp f
proof
  let f be non constant standard special_circular_sequence;
A1: (Cl RightComp(f))` misses Cl RightComp(f) by SUBSET_1:24;
  Cl RightComp f \/ LeftComp f = L~f \/ RightComp f \/ LeftComp f by GOBRD14:21
    .= the carrier of TOP-REAL 2 by GOBRD14:15;
  hence (Cl RightComp(f))` c= LeftComp(f) by A1,XBOOLE_1:73;
A2: LeftComp f misses RightComp f by GOBRD14:14;
  Cl RightComp f = (RightComp f) \/ L~f & L~f misses LeftComp(f) by GOBRD14:21
,SPRECT_3:26;
  then Cl RightComp(f) misses LeftComp(f) by A2,XBOOLE_1:70;
  hence thesis by SUBSET_1:23;
end;
