theorem
  P is_outside_component_of L~g implies P = LeftComp g
proof
  assume
A1: P is_outside_component_of L~g;
  UBD L~g is_outside_component_of L~g by JORDAN2C:68;
  then P = UBD L~g by A1,JORDAN2C:119;
  hence thesis by Th36;
end;
