
theorem Th12:
  for C be Simple_closed_curve for n be Nat st n
  is_sufficiently_large_for C holds C c= UBD L~Span(C,n)
proof
  let C be Simple_closed_curve;
  let n be Nat;
  assume n is_sufficiently_large_for C;
  then
A1: C c= LeftComp Span(C,n) by Th11;
  LeftComp Span(C,n) c= UBD L~Span(C,n) by GOBRD14:34,JORDAN2C:23;
  hence thesis by A1;
end;
