theorem Th61:
  for S being being_simple_closed_curve non empty Subset of TOP-REAL 2
  holds Lower_Arc S c= S & Upper_Arc S c= S
proof
  let S be being_simple_closed_curve non empty Subset of TOP-REAL 2;
  S = Lower_Arc S \/ Upper_Arc S by Th50;
  hence thesis by XBOOLE_1:7;
end;
