reserve a, b, c, d, r, s for Real,
  n for Element of NAT,
  p, p1, p2 for Point of TOP-REAL 2,
  x, y for Point of TOP-REAL n,
  C for Simple_closed_curve,
  A, B, P for Subset of TOP-REAL 2,
  U, V for Subset of (TOP-REAL 2)|C`,
  D for compact with_the_max_arc Subset of TOP-REAL 2;

theorem
  A is_outside_component_of B implies BDD B misses A
proof
  assume
A1: A is_outside_component_of B;
  BDD B misses UBD B by JORDAN2C:24;
  hence thesis by A1,JORDAN2C:23,XBOOLE_1:63;
end;
