theorem
  P is_inside_component_of L~g implies P = BDD L~g
proof
A1: RightComp g = BDD L~g by Th37;
  BDD L~g is_inside_component_of L~g by JORDAN2C:108;
  then
A2: BDD L~g is_a_component_of (L~g)`;
  assume
A3: P is_inside_component_of L~g;
  thus thesis by A3,A1,A2,Th39,GOBOARD9:1;
end;
