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 Th42:
  for f being non constant standard special_circular_sequence
  holds (Cl LeftComp(f))` = RightComp f
proof
  let f be non constant standard special_circular_sequence;
A1: (Cl LeftComp(f))` misses Cl LeftComp(f) by SUBSET_1:24;
  Cl LeftComp f \/ RightComp f = L~f \/ LeftComp f \/ RightComp f by GOBRD14:22
    .= L~f \/ RightComp f \/ LeftComp f by XBOOLE_1:4
    .= the carrier of TOP-REAL 2 by GOBRD14:15;
  hence (Cl LeftComp(f))` c= RightComp(f) by A1,XBOOLE_1:73;
A2: RightComp f misses LeftComp f by GOBRD14:14;
  Cl LeftComp f = (LeftComp f) \/ L~f & L~f misses RightComp(f) by GOBRD14:22
,SPRECT_3:25;
  then Cl LeftComp(f) misses RightComp(f) by A2,XBOOLE_1:70;
  hence thesis by SUBSET_1:23;
end;
