reserve m,n,i,i2,j for Nat,
  r,r1,r2,s,t for Real,
  x,y,z for object;
reserve p,p1,p2,p3,q,q1,q2,q3,q4 for Point of TOP-REAL n;
reserve u for Point of Euclid n;
reserve R for Subset of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL n;
reserve D for non vertical non horizontal non empty compact Subset of TOP-REAL
  2;
reserve f for clockwise_oriented non constant standard
  special_circular_sequence;

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;
