reserve n for Element of NAT,
  V for Subset of TOP-REAL n,
  s,s1,s2,t,t1,t2 for Point of TOP-REAL n,
  C for Simple_closed_curve,
  P for Subset of TOP-REAL 2,
  a,p ,p1,p2,q,q1,q2 for Point of TOP-REAL 2;

theorem
  a in BDD P implies not east_halfline a c= UBD P
proof
A1: BDD P misses UBD P & a in east_halfline a by JORDAN2C:24,TOPREAL1:38;
  assume a in BDD P;
  hence thesis by A1,XBOOLE_0:3;
end;
