theorem Th15:
  L~f \/ RightComp f \/ LeftComp f = the carrier of TOP-REAL 2
proof
A1: (L~f)` \/ L~f = [#]the carrier of TOP-REAL 2 by SUBSET_1:10
    .= the carrier of TOP-REAL 2;
  (L~f)` = RightComp f \/ LeftComp f by GOBRD12:10;
  hence thesis by A1,XBOOLE_1:4;
end;
