
theorem Th21:
  for C be Simple_closed_curve for n be Nat st n
  is_sufficiently_large_for C holds L~Span(C,n) c= BDD C
proof
  let C be Simple_closed_curve;
  let n be Nat;
  assume
A1: n is_sufficiently_large_for C;
  then C misses L~Span(C,n) by Th8;
  then L~Span(C,n) c= C` by SUBSET_1:23;
  then
A2: L~Span(C,n) c= BDD C \/ UBD C by JORDAN2C:27;
  UBD C misses L~Span(C,n) by A1,Th20;
  hence thesis by A2,XBOOLE_1:73;
end;
