
theorem Th17:
  for C be Simple_closed_curve for n be Nat st n
  is_sufficiently_large_for C holds UBD C misses BDD L~Span(C,n)
proof
  let C be Simple_closed_curve;
  let n be Nat;
  assume that
A1: n is_sufficiently_large_for C and
A2: UBD C meets BDD L~Span(C,n);
  UBD L~Span(C,n) meets BDD L~Span(C,n) by A1,A2,Th14,XBOOLE_1:63;
  hence contradiction by JORDAN2C:24;
end;
