theorem
  P is_outside_component_of Q & R is_inside_component_of Q implies P misses R
proof
  assume
A1: P is_outside_component_of Q;
  assume
A2: R is_inside_component_of Q;
  (BDD Q) misses (UBD Q) by Th15;
  then P misses BDD Q by A1,Th14,XBOOLE_1:63;
  hence thesis by A2,Th13,XBOOLE_1:63;
end;
