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 Th21:
  Cl RightComp f = (RightComp f) \/ L~f
proof
  thus Cl RightComp f c= RightComp f \/ L~f
  proof
    let x be object;
    assume
A1: x in Cl RightComp f;
    now
A2:   now
        assume x in LeftComp f;
        then LeftComp f meets RightComp f by A1,TOPS_1:12;
        hence contradiction by Th14;
      end;
      assume not x in RightComp f;
      hence x in L~f by A1,A2,Th16;
    end;
    hence thesis by XBOOLE_0:def 3;
  end;
  (Cl RightComp f) \ RightComp f c= Cl RightComp f by XBOOLE_1:36;
  then RightComp f c= Cl RightComp f & L~f c= Cl RightComp f by Th19,
PRE_TOPC:18;
  hence thesis by XBOOLE_1:8;
end;
