reserve i,j,k,n for Nat,
  C for being_simple_closed_curve Subset of TOP-REAL 2;

theorem
  n is_sufficiently_large_for C implies cell(Gauge(C,n),X-SpanStart(C,n)
  -'1,Y-SpanStart(C,n)) misses C
proof
  assume n is_sufficiently_large_for C;
  then cell(Gauge(C,n),X-SpanStart(C,n)-'1,Y-SpanStart(C,n)) c= BDD C by Th6;
  hence thesis by JORDAN1A:7,XBOOLE_1:63;
end;
